{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.ndimage\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (a) face"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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eN6sqeeONN2zh7dbWlhWPX79+HcfHxwZ2KLqorm0kMituppWiQLD8jJ0NWDZI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\nkCd0Qn1EJwx5QifUR/T/AXHPXNzSIs54AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x261d5979240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#read image\n",
    "face = scipy.ndimage.imread('data/low-rank_data/face.jpg')\n",
    "plt.imshow(face)\n",
    "plt.set_cmap('gray')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def low_rank_approx(image, r):\n",
    "    u, s, v = np.linalg.svd(image)\n",
    "    s[r:] = 0\n",
    "    s = np.vstack((np.diag(s), np.zeros((u.shape[0]-len(s), v.shape[0]))))\n",
    "    return u.dot(s).dot(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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L10g3gLRVc4LECRYLip8y8HVPnjwZn7hwEscD5Os5r8hkBC0/s7V0qR1HuY0ECYnJHwtO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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x261d4594198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "face_lr5 = low_rank_approx(face, 5)\n",
    "plt.imshow(face_lr5)\n",
    "plt.set_cmap('gray')\n",
    "plt.title('rank-5')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HIQ5E7toToYG2xYEEfIVJEBKXl5c6OzvTaDTS0dGRRqNRctZ4mIFC/R4Gms1m6Vqfs9Vq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\nNxFt7PhA+6ayFQzJZDIxDr/8+cFms5mYotfrpefWmMDT01NNJhO9//7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+TN88e/ZMh4eH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\npxmifwBZC18PjfyXfwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x261d56cdc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "face_lr20 = low_rank_approx(face, 20)\n",
    "plt.imshow(face_lr20)\n",
    "plt.set_cmap('gray')\n",
    "plt.title('rank-20')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qhv6iFqtTyFhzO5lMV+8rFosWldza2kKn0zFFQzdkMBhYBZYGaljzSgvPMVLB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\n2k7bCWr/Hx7YpmX9OB/xAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x261d17bbeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "face_lr100 = low_rank_approx(face, 100)\n",
    "plt.imshow(face_lr100)\n",
    "plt.set_cmap('gray')\n",
    "plt.title('rank-100')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (b) MSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_MSE(image, rank_range):\n",
    "    all_MSE = np.zeros(len(rank_range))\n",
    "    for i, r in enumerate(rank_range):\n",
    "        image_lr = low_rank_approx(face, r)\n",
    "        all_MSE[i] = np.sum(np.square(image_lr-image))\n",
    "    plt.plot(rank_range, all_MSE)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XIroP9PHkds3eRaQxNES4X/PeBczMZ/i7jd1RlyIiMiUaItzz2TQfu/B0Nrz4Nof6ddaM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\nRBLo/wNktvExRla0gwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x261d56654e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_MSE(face, range(1, 101))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (c) sky"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FVopm+l8dz0A97lB9VLyn3Ix6guofjKZhfsotGOmim0IBwMOHD1fM5oQSD+vK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x261d59741d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sky = scipy.ndimage.imread('data/low-rank_data/sky.jpg')\n",
    "plt.imshow(sky)\n",
    "plt.set_cmap('gray')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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oegpKZUYFWDWTZjaLU08yVY7ZMdrJ7VKAKatHnTlf3TKnKnzG5k4cu2k/KVsr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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x261cd85c8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sky_lr5 = low_rank_approx(sky, 5)\n",
    "plt.imshow(sky_lr5)\n",
    "plt.set_cmap('gray')\n",
    "plt.title('rank-5')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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iPtWmDO4w/dWd0CCGBrRiDPm1iAr6qRT16qNO0R/uO7snaqZH4CrKDPPUaTYO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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x261d5974c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sky_lr20 = low_rank_approx(sky, 20)\n",
    "plt.imshow(sky_lr20)\n",
    "plt.set_cmap('gray')\n",
    "plt.title('rank-20')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SWl4U56piOaRViKUwyeMdh2bqQSiIzqfWqTy5x/N2vZ80ZJoB5fien593XlfA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\nFnF3LZ8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x261d3f48c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sky_lr100 = low_rank_approx(sky, 100)\n",
    "plt.imshow(sky_lr100)\n",
    "plt.set_cmap('gray')\n",
    "plt.title('rank-100')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (d) find the threshold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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84hNW4dLv9y3kZr0yDbJSGlzUUi6XUa1WLQcxMzODWq2GGzdumFPZ2tpCLBZD\nsVi0cJcJOCIURgyK7Djh2aekwOhABoMBZmdnsby8PFarrFsxsEqCkRGFURHHicZaSyGZvFLqJpVK\n2aRgHoFGhw5HF7woHxkmr4j2wzI2GpdJ5WyPWpgcZ58ymUqjQCOvi4tYB57NZo1GIWBot9tWiJBK\npSz65ZqPWCxmKLtarY4hdkaW1I1MJmORFo08DfiNGzdw48YN/NEf/RE2NjYAwMp8GY0A4840l8uh\nWq1aMpN18OT9iX652j0SiaDRaIxF3lrdoyuHaWQ1AcskKqMmUjl37txBt9vF3NwcLly4gEQiYfMT\ngNEt1C01qoy6ms2mvZ9KpczQ83vdbncMzfM3bQdRPW0adZuUW4joqatq/KnH/GzoGJTOOUxOhKEn\nvaGDyooXVhyk02nrLE1ysDKAoRUpHCZ2uSiD36V3Jhonz00noIMHYKxEUReybGxs4FOf+hTW19eN\nTuHfHGBdiETHAexXSQwGA+zu7qJSqaDT6SCRSNjfRDyJRMJ4VUU0RPVEYOyzZDJpfKMiCOXDWdEx\nGAystJM5B0Yxyi8q36hjxs9xQlDByV+qYupiGobF7HPdWyhE4SH3/k4UGg2t4KBD40I8AgEtGWVl\njho+Xo/Giv+nUimjPxkttNtt5HI5uyZBB/tbcyi8587ODlZWVvClL30Jm5ubBla4IJBzhlU6RMP8\noeNgscDOzo4ZJiZPgX3DzfUdROYca1auMRqgkSSdo0lnAJb0Z2EFqat+v48zZ84gnU6PRZcqfF3B\nkOpgWCCgDoj6Sf1m0YGidNod6rsaeP4OeXqCGF4nlOOCmBNh6Pv9PtbX160kkcmOSCRivCG5N4ZY\nVCw19Jroq9VqqFQq2N7etkSOKjcw7NRSqWQLllqtltX+MotPPq7b7SIWi2F3dxef/vSn8YUvfMGM\nbD6fx61bt8wQc/KQ76PD4uQl9cOQnnwnuXYmwnitTqeD9fX1sYVjfJ+fpxISbRGZ0+ByoRkRBScR\nK4rq9TpWV1dx9uxZ5PN5Q1haB60ySUk1/6EonzQXfxPpE82zTYwoSGWF/PykZKvSNyfRIQwGA9y8\nedOqVWjUubJUF8AxAiMvTE5dowDmZGq1Gra3ty3XxMoQrVaanZ21NSjVatVoCep2u902umhzcxNv\nv/02vvKVr+C1116z6hlG0AQwpE3K5bLNJVaRafUXV5gzcmk0GshkMgBgFXVE+4z6WAShc3xxcdHK\nMqlfrVYpqxOZAAAgAElEQVTL1tWQ6m21WlaBxzxHp9PBzs4OdnZ2kM/nsbS0ZBSWlgLzOWjgWSZN\nvSetq/SitpFAkIlyABZFMOriwkdGDPwOHQH1N9xEkU4lpGw0sjmKnAhDD8BKzKLR4Z4bRKBc5s8K\nApahbWxsoFKpWCcySUNF6HQ6tgiK3LUmAYmodGsARgBcFMKOZknliy++iJdfftlQAu9/69YtS4Jq\n1YuWxDHkYzhLIx+NRjE/P2+ThIhCFatQKGBubg4AxhK7xWLR9s4h78rvsBSs0WiMoXqlfGiUtTLm\n5s2biMWG+41wX5xJq/CodKEo+qDRodJSsYnuOMFZPsfP8jOTSsomhbHappMoNMQ0QJygNOBMEmqJ\nL3ULGHLeWllDRFuv18dq3qk35MD5Pa0TB2A0DvV+c3MTd+7cwe3bt60NnCs7Ozt3RRmMqjnntHrF\ne4/NzU1D4dyegLQiDRnpy7m5uTG+m3OO8/rWrVuW9+GzxWIxVCoVuxYBEg0mKStSLclkEs1mEysr\nK2PrAIrF4lhSX5+Nz8vn00IOvsd2s220MQQvrPwhcGEkRYfHcVPd7vV6E6vJwvyCzo2jyIkw9M4N\nV7VpEo7cMn9zvw+iEW7YlUwm71ogRO85OztriSwt/dOabyoRB47cOdFRu93GysoKXnnlFbz00ku2\nF8fGxoZx0uTOaUSJhhk5cDKSflldXUU0GsXS0hJ2dnYsv0DUk0wmLXdAtNtqtayeWimhXC6HdDpt\n2zDMzc0ZOmHFDhEIF+BoFQrL+fb29gAMcx6xWAw7OzuIxWKYn5833j8cs0n8OMcgDDcV9fM9IkSi\n/bC8DYA5zUmhb6j8J1GYjCUAAGB0A5f/0yiSFtza2hrby4XJdPYL13Bwiw6iVGDoVNLptBlLUhb8\nPg3uYDDcLuP111/HrVu38Pbbb5vutlotM5IAjFZku3kNzccQwW5ubmIwGGB5edkqvkh3MBGtJaPM\ntxUKBQNlNNp0JET+Gh0oKubiLEW++uykmkgRA7CSSuaN+DyMttgHYTRLMKrC7/LapNIIvjR3xvZw\nDNSwH8eAHzeKPRGGHoAlMdl4rUnlIirN5M/MzFiow0QPsD8Z+B75Mi37oxHhQGrCr16vY2FhAdvb\n20in0/j4xz+OT3ziEzbwjBi894aKWV3DlYWFQsGQCZWZ3DgVhXt6sCyNf7ONmgAit0pF1rI7Oilu\nq8B2MLpQFMmIguVy6uRKpZIl/JwbVoJsbGxYVKX8MkX7klVG2pf6m58Jq4IYNmuFjUYgYdhKY0NR\n9BPSPJpUf1xCsMJtPQBYOA/AckhE7N57FItFzM7OmqGgkK/XLbn5zDRQjBwZBROdMlKlbjSbTXzm\nM5/BZz/7WUv2c9NAOgHqFcdHo0Zgv8JH17sAsKouUiyae/DeG6KlU+K8JqUCjC8oUiejJYZ8NtbO\nx+NxA4ScM3wGcv2RSMQcEKuXdBW8PhP1jt/j8+uzcAx4L9VHto92jPOZY61VanQEek29T6jbxwU2\nJ8LQk1Kgx9aBo3LTmNNwK03BzuKE0TI9TYhMCvvVWJETrNfrKJVK+Imf+Am88MILaDabxh3q9QAY\nz81FIJwYFKJ58ozA/pL2lZUVq6EmUtEkGycIB5woT5N0pLz4zKSFABh66na7WFxcxNbWllXpkCsm\nogEwVuHDSqM7d+7gmWeeuYtG0WStKvdBEhp98px0bhohaOSlk5rjNIm6UeeiaP9xVt0oiiUaZ1if\nTqdRLBbNQVIXqfs0EHxdI1Glt+jQGDGo4+B1lddttVr4yEc+gs997nOWBNUSTc4hYF9/VTjWujqb\nlGI+n0culzPdLhQKtiCqXq+PVbuwjdw8jXOHCd3NzU17Nhpqzg/mHkjbMAFNW0C9mZmZMVq0UqnY\nc3nvsbOzY/QW5zOBF/uRIE3LJ9UYU0JbwoQwgQ1pZP5PndZ76/f1HqEOsz/ecclY8oksBeP+LUQg\nutKVRoGdRANH4WuhMQ+9oH5HXycifu655/Dqq6+OZeNLpRJarZYtVFGDx47PZDJmkJWOUAUfDIYL\nS3Z3d7G8vGyJS10EAtxd9hVWtRDhMn+haC9cNMUEE0sllT7hhOUEI7qhVCoV2xSObQnH76gKN4ni\noeGm0WDVEvtMJx4wfcc/vnfQ+49aIpGIJdez2SyKxaLVk3P/Ghp1RY0EE0of6PPzPUa/mvimgeE1\nyA2n02ns7u7i85//PN58882x3BF1T/VU32PkquNG2kHLA733tuJ3ZmbGjCOdllJwvAe/y7nCQgFG\nKCzHBMYXEvG5qes06LwmdYllp4z6KZyfkyhDzStoElrHgX0xqViB48S2MU/D9mm5rQJWfm+ark8q\ngjiK3Jehd869DaAKoA+g573/RufcLICPAngCwNsAvsd7v3PQdSKRiFUe8IAMGnauQKOogvPvaRxt\nyKVNQp38Lgd6MBjgx3/8x/HlL395jK4B9vliLvLQsJYTjIiMfD1pHvKNlO3tbatbZk0yk8icpMrt\n08lx0rGCQkNZovO5uTkrheNKSLZzdnbWlK/VaqFWq9leITs7OygUCmg0GjbJEokEbt68CQCWGCfy\nUIN/FKOqE0KTtGGyl9enYVCko+M6Cbnrz/0Y+gep23Nzc0in01haWsITTzxhKz3VwFPX+Sx8TkXk\n6lBD50pUS4OtESeTkevr6/joRz+Kz3/+82OrVWlsCAQUTJACIg3ISikaUuoA6RjNq3GNCEt9yZEz\n58bIUvlxzhtGwNTrZDKJQqGAvb29sUiXoE+jWjow6j+j3EKhYPQS28/Vxsx/ESTyfeoQ5zgrfdg2\ntUOUSdUy/DydFqklvR9Fx532jc6Q8kgN/Uj+nPd+U/7/AQDPee9/zDn3A6P//9uDLsDKk1RqeAgD\nK0pI0QB3LxvWcOeoiJKKoaig0+lYNPGZz3wGv/7rv47NzU2kUilTNpaDAfulWLrBERVvdnbW0IH3\nHru7u8aLcxIxxOY+OZubw65jpMBQn4lmrVOmx1e6iGE3JwQXtBQKBUvcttttDAbDJeJMZIVcdyQy\nXG3M+2skwoUwRIxaKjoJabCPVXkn8eTh52gQeB8mxjXMjUQiNkHYH5xU4WS4Fy4zkPvW7UgkYusT\nWDOve7OTOuFY0+hxsiuCVnpL6UOKGu+wvv3Tn/40Pv/5z+OP//iPUSgUsLa2Zgv0CCJolIl8iXhJ\nE7JSZzAY2PbY8/PzxosT7CQSCczMzGB1ddVKEMnV66JEjRRo/HTjNz7LzMyM6XatVjOAxJ1fgf1C\nBzouJvlJ81DvCTaI2OkEWODACEn7X69Fx0IwNs340vBT//T6StHxM9Rrdf4c69BxcH48akMfyncB\n+LbR3z8L4FM4wmTgQKmh4KBMQ2fHncghPw8M64E3Nzdx/fp1/NzP/Zxxcnt7exYK0tMT7eRyOaNA\nuLvlYDAwxSOi4J7b5Bd5LToRKiW3R+Bzaj0uFUATSzSAwP55m+xDXptlcvxONBq17RRoREulkm1q\n1ev1kM/nAWBsJawiJS7EUiM7SaaN1yTF1BwE+VqOfb1eH9s/h32p9w7vo+hJ+c4HJPek20yS8/nY\nzpAb12fX3AcNTrhSlIaeVJcWMDQaDTN4zz//PJ577jmsra1ZEUG32zV+mggbgI07r5NIJLC9vX1X\nFEWjrytC4/E4SqWSreDl9UhX6PVJf7KcmBGv7tWkVI86fyZ+6SA4L5m0JU2TSqXsqETSQexfPk+Y\nH6Kj5f2UWqTRDwsNQoCheqcAh0CG99WFYJxTdCAh+6DMxb2Al/s19B7Av3bO9QH8pPf+pwAseO9X\nRu+vAliY9EXn3IcAfAgYogKGjxw0YHw3t9F37uLe+fe9yubmJhKJBH7kR37Eaty5L4cqKReysLKG\naFlpDi2hA2AoBsAYt080pCv1tCJifn7ekqxE5ES12j9cXKbHFyrnDsD2G2fbGMozcqIR5clYRFnA\nfgipnC138ZwypvZ3qOTAZOosRP10aoxYiP6IeDX/ohNW78+JEkYbx5QHptvk3LltNKtaaEyUa1ak\nrg4zTNIB48c56nOnUinU63VkMhm89tpr+OVf/mVsbW2Z4e71htsGc8dU7i4ZUim6v7s6fI6HRmL8\nHs+V5Xmu5NLpFLj3FBOwHEfNPxHZMlKt1WpWvcbPdbtd29+KIITt50IxOlVug0KDTqeka2sGg/1t\njjVZ7Eb5Mz4n+5iR5iQuXfMVmnzltdh+YGgXeB41dUEdvF53ks07qu27X0P/zd772865MwB+xzn3\nmr7pvffOuYmzbDRxfgoArly54ok6O52ObYkK7Ne/h1zXvT4wv08vXSwW8eEPfxitVgvlctm2MmDl\nCZWIZXA0mNvb22OJM1IjuVzOjmsj2k8kEpidncXs7Cy897bilhQIUQwPYeDmaKRHisWiIRtGD6wt\nBjDGqxLZ0OFo7TajEioqUV0+n7cohrwrEQYVmxOJaGeSKCU2SSbRNyE9QWNPB8fQm4Zf9OeuqCKc\nDJoovAd5ILr99NNPe/Yln4l9yHbSMGhCVnMT03IhyuXTiHBvnWKxiGq1il/91V/FW2+9hcuXLyMe\njxsoINVHQ0TjQqPPKJaAgWWI4YE23g9LncvlMgaDAVZXV21LA5YrUj85p5US4fwmkuXzxeNxy13R\n4cTjcSuJJB1JWog0CPuZFMvi4qIloZXK4sZjnIt8Fh0H3ZZB1z6Qp+f8pOj/0woWQkPPtQOaE9Fc\nnxp7Hf/jcvT3dcaa9/726Pc6gF8D8D4Aa865pVGjlgCsH3YdDac0m6/vW4OnGJl7lWaziVdeecV4\nPyoC78/JoEkerUagc6LRBWCHn3Cy6F4m3ExN0RC3XmAITI6d6IuHoXADKJ6Jy8VVnEREiapsREEa\ndQD7yVAARilxAlKJ+ex0RlyIw+jhYYhyksq9sy18LfyZJvdK2zwo3Qb2E3n6HApeNG/EzwAHn6w1\nasMYguS4E6lubW3h5s2bVtKpho7t0kgC2DdW1F3WlTMvQsDAzf0YZTHRymSnVrRwXyW2j3QcAEP2\nfGbv/djamEm6yDxA2Ffe729brny6VubptdjnWqevJZA6F5RSUQ5fxyKsjtL32TZeK6wuU4fL30rV\nTGMzjqrf94zonXNZABHvfXX0958H8GEAvwHggwB+bPT740e5Hvk20gMMoxi6hwY+DGuPgtoUMXLQ\nPvnJTwIYUhy7u7totVrI5/O2zUGr1TIOOxKJWEULd/yLRIZ7vafTaTPWRCs0kLz39vb2WCUAsM9J\nkjZiPTFDXxpzbhnAI90YHquDYkUQ70sOmIs1EomEJXrz+bz9tNttnD17FolEwvZOJ69ZKBSwvr5u\nPD83z2J+ghNFk02TKmkOGqNwbDnB6KTIzWqCi45JX6deqNG7F1rvQeo2cy50yKojRIcAxqrLVE9D\nx00hFaJ9xvwMAcUf/MEfYGdnB6VSyfI2LASIx+OGcnU/JqJ50pY04J1Ox+ragX1wQPDDKDwWG+4H\nxWIDXd+hlCy/y2dlhEo95+Hp1C8aNLaN0ZwemcjiB5aucg8onuvAE9ZY+cMKMiJt6hyplHCjRCaL\nw0SsOmk6cI2Gdex4H+bt6Nj4Pf6tcyiM6A6LnCfJ/VA3CwB+bTSRYgB+wXv/2865FwB8zDn31wBc\nB/A9h10oEomYUeN+MxxwIpEHgeR1oCKRYZXJb/3Wb+Hs2bNj2/+Wy2U7yYn8Ho0xKQTl0WhwaHS4\nMpYh8tzcnFXDAPtbobIkjfuc5HI55PN5tFotzMzMWIhIw0sjDsA4/Vwuh0qlYif5nD9/3rhgYH83\nzng8jmKxiPX1dUNMdKA0+NFo1PY7Jx9Zq9UsD8CQt9vtYnt7G4uLixYqHzQ+mgQLZZqyEgExeahV\nCLyXliaqQdeJcI+I/oHpNrC/QI56zdORwhJLjSKPkoNifyrXzHFdWVnBSy+9ZBVsTF5yfyRSgKpP\n1CnqO9/jVgIEN4xC2feDwcA2TeN38/m86TU5cUY1asRisZhtvQzsr4OJRqPI5XJj21jH4/Gxc3EZ\nqQIwsEMQwKiX7ec8pdNisQSjaEXvzMHpJnvURbZdoy3qY0glhklajiXn9GAwsBJnYB+8cv8t/qhT\nmZYAPkzu2dB7768CeO+E17cAvP+41ws3t2o2m+aVj2Lkj/IZRYjxeNxOler1ejh37hxee+01JBIJ\nbG1todfroVKpYHl5Gf1+31D0zMwMdnd3bWMo8o9Kz1CItjkparUa2u22HabA6gF+hzXti4uL2Nvb\nMwUHhpOaDoTP65zD3t6eoUFujsbSTyakiL6Y5HziiSfG0AcNNgCjZliHPzMzY2fY6i6Dm5ubqNfr\ntmPgpDEIUfUkg3WYoee1WZvNZDJRoSp8SIPcazL2Qeo20Z3uQEmwQbpBUZ62PWz3pEoncsrAPs2Y\nTqextbWFjY0NM3x7e3uGRJkE5U6opB15YhSNfqfTQaVSsbMYAJhTZzKfwoRpNpsFAFsQyDnhnLPi\nAVaz6fgwAmDk3Gw2zQCWy+UxDp6RA4FHIrG/Fz83/2N/zs7OGsVE+onXZYTLxDPzPpqYDfMRwL6D\npXNWneOYT/pbE+o65tzGmpEr+4FOiNfR+UPndFQ5EStjAdjqV27oxWw0kcSDEHpIcmQ8cf7cuXMA\ngOXlZYskLly4gGq1ivn5eVy/ft3oHHr5Xm9/NSqTsJxETN4458aWXQND418qley4QT045JlnnkEu\nl8Mbb7yBixcvmvOLx+Njq1uJKrgknDwk968hyqFyZzIZFItFNBoNXLp0ydYtUNGj0aglZZPJJGq1\nGra2tlAoFHDjxg1zdkTONPbh9gUHSaioRxEquibxuHkWDb2u4FXRSXivPP2DEt3SgKcqEVFzLyLl\n7rWaSNGmGoywEo2JT77Hg7kXFxethJMolRvXeT9cxcrqG1bOOOcsH3TmzBnbdE8rx5hY1r2k0uk0\nZmdnsbm5adGoHihOxzwYDEzXqLdcFEWDSyCi9JYWGLB/UqmUHdYDwLbYjsfjmJ2dHTvCEoDtm8Vz\noHV3Tc4jllbzHgRM1CmlzBTZawUPn2FSBRtfI7LnGDIHQt3W7yiFdy9yIgw9FYWDwu1XOcgs59NK\nBX7voIcPDQspE24Z+/LLL9vmaDycmAcMb29v2xGD5Ay17pm/q9WqHe5dq9WMv2d9MLdcbjQayOVy\nKBQKtiT+1q1bRplcvHgR0WgUb731Fi5dumQGl4abWxmQR2W54bPPPotkMolr165ZnTvLy+go0uk0\nZmZm4P3w1KJz586ZwnJxFI1+t9u1ifP2229bXTRDTdYnsx3kVunYqJBEbio0Ipr0VcpC0alSPWwr\nD4vh6kJN2tJA6vc0cfu4xDlnFBtPPyMNR6oDGDdeuhhGeXoavjBZSxSq1MLa2prx7EoVMcdCQEJ6\njsae3DW5eaJMnpugJ4axVJKRbjqdRqlUQq/Xw+rqKhKJBBYXF5HJZBCLDQ/XLhQKhli997bfz87O\nztg2B/l83nZO5QEijJwZYbJAIJfLIRKJIJfLYXZ21tYHML/HeQDA+p8/nKesWuNCQ0br1FE14mHR\ngvL81HuOC4V6qEae48sIRdepsH80MuCY8/vHAU8nwtAD+2g7rFDQ7PODEEXFXEDCiaO/ud0quW/y\n46VSyfh7IigqOL+ji6MAGOfNMz4pXAZ94cIFLC4u4o033kA8Hkc+n8fe3h6KxSKy2axtNAYMuchs\nNot+v2/nY6bTaZTLZaNwWP6pqJFbLSwsLCCbzVokoQlA7oDJY9hu3bo11md8XmCIpKrVqu39HUZd\nR+GY9bOHjTEnEisvtCZ9kiE/Tlj7MEUrNbQqhs+rIbg6PKJGorqQhuJrSgfQWHW7XaMfOX/ojPv9\nPm7fvo1sNovZ2dmxJf1MetKpJxIJO6yb7SRg4cpVlsAysqNjI8XGrU14xCCdVTabtQiYkTKLFPiZ\nwWCA+fl5m5eMquv1+tjJcdRZ5rjYr2xzJBIxEBOLDXdjJU2lFUcEGlxwpjt4Kk/Pz04bFzrqUJ9D\n0KGfYQUO9TqsMONY6zUfVTL2gQqNDsMX7s+uvPpBchRHQC+fTCaxsrKCmzdvWs0xQ7iVlRVDPeVy\n2XaZJBp58803rbab6D+VSmF1dRWx2PBg8PPnz8M5N3YOLgBbDcsVqMvLy2g0Grhy5Qpu3ryJzc1N\nPPHEE1a+mE6nbd/9WCyGhYXh+pxUaniq1KVLl4yTZX9xojzxxBNWMcT6ey4mYWhOpEP+nhOk3W7j\n3Llz2NzcxBtvvIFqtYqzZ8/adrv1eh1nzpyxnEO4sAoYRx6HjdthFIsaeU4IIjLdbz3kvI9y/4ct\nRHHkvaPRqNEeTAoqmqcT08VhWpIHjJcnAvvbP/MeKysreP31123saUB3dnbMuHH3x9u3b9tZEKQ1\nmBtjxMAIYHZ2FktLS4hEItjZ2RlbSEQjydd4aM3S0hI2NzextbVlXDkNNlEzT7riTq6MLqLRKPL5\nvOkcK4KWl5fhvcfq6qoluOPxOM6cOYNodLgCPJlMWnShEV88HreIdW9vDzs7O1hcXLQ8HJ8/EonY\ntgk06sB+5BWWYIYRaGiQdZ2AOomw3JKRqyZ/GfXyf/19VP0+EYaeHKNuRVytVk3xjmLoJ1E4Iarj\n/xsbG3juuedseTQdC8vMiHZbrRZu3Lhx126PDPGosHt7exa+hgu/WM5FRMcdC0lJXb58GRsbG1hb\nWxvbo355eRnXrl1DNpvF4uKiVSHE43E7zPvatWt2oDR591wuh7W1NWxtbWFpacm2aWWppFbzsL9Z\n+9zv9+1glVarha/6qq+y/U/6/b7tUwLAogx+l8k0VTwtLZumkGHZ5WHGnlRRGOpOKrE8CUJkS4fM\nBUv1eh3NZtMQsxoC9glzE6o7FF0HoYhvfX0dv/d7v2cnhdFIcv7s7OyM7eMEwDa1o7HSdRWcg6VS\nCdls1mgTrbJhe+k8iOp5IE+lUrF9rEhfkk4iUMpkMqafXPTFOvpoNIq5uTkrE93d3UW5XMYzzzxj\ndE42m0WpVLJ8B50eS4sBmKMh9cSxYKRK1E/QORgMbG8d4O4VyErbAOPbZ4djo3NDkbnqLXU7Go2i\n2WyaLeR3ef17oSRPhKHnYHLjJ4Z59NY0wIr+tEOnOYFJVSCxWAxf+tKX8MILL6BaraJYLBoiYWnj\nYDCwlXflctnauLe3Z3xgp9OxFbS5XA7lctmqafh7dXXVFIXlmaz35RbFrCJYWFjAwsICtra2bEvg\nJ554AgCMQ2XC7ebNm0gmk5ifnzfje+fOHdy8eRPnz5/H/Py8nddZLpeRTCYN7XBlJhPf5O2JkrVk\nrVgs4qmnnsLW1hZ2d3dRrVaRzWZtDxoqfLPZHENGVGwi0HCstUQyrBEOE1r8m2NOFKyons+hZ30e\nl8N8WKJ0AMv+Go2GcbPUbc1VAOMVS0rPEPFTyLtHo8O9gV599VV84QtfQLPZtM3AmFthQp1VN0ys\nam04cy07O8NNOfP5PM6ePWtRG88rBvYjKG6OpuswlpaWzBiROweAxcVFeL+/SIlVPaxC09LGpaUl\n28d+c3PTyjZ1989yuYwzZ84YWKvX6waIeH9GCDScXPhXrVatIAOAfY5jQT3jfGH/hch60phrMUA4\njvwMsK//mpBnLoo5BOpDmKh/R3L0wPgJ6MB+VvpBITSGR6+99hpu3rxpxqjRaNj2vdVqdazmd2Nj\nA/1+30JBKgUVhlU3nMilUgnpdBrXr19HpVKxk5s4gRqNBvb29vB1X/d1xsvTmdXrdVy8eNEMdalU\nQiqVws2bN406uXTp0ljlT7fbxeuvv45r165hZmbGJviVK1eQzWaxs7NjlBgVkwbHuf39V/jMWirZ\n7/exuLiIhYUFXL161ZLAWprJxDlLP6l4YWh7LxI6dqVjmMOZxtM/bgNP8d4bumSehdVEDN0VGfJZ\nQuoG2DcW5NL5HRqndruNN954A9euXbPFh61Wy0oOG42GfSeRSGB9fd3Gnjuvsk9ZGME8U6FQsDNW\nSZlo3giAbSdw+fJlLCws4K233hrj8GdnZ61ai5SS/s5ms1ZDzkKHF198EXt7e5YTmJubw+zsLObm\n5uyAHXWSjCoIoAjY2I9scy6Xw+LiIu7cuYPr168bVcS2ERTp9iJKtSg9OIk/D42wonk6X9VZLSAg\n1aSiZdX8fZwqnBNh6HUSU8G1np70zf0aeyLMq1ev2iZPuv0uN/Zip3IHSO4nDsD2rSkWi1haWsLs\n7Czy+TwqlQq2t7ft0PJKpYJCoWBHqvV6PaysrCAajeI973kP9vb28NxzzyGRSOCJJ57AlStX8OST\nTyKTyRgqYmnpN3zDN+D27duWSKWR997jC1/4AlZXV7G0tITl5WU8++yzVkkUiUSM9mFpW7h5nNbP\nU5nJ4XrvLUS+ffs2Go2G8aG93nBjLDoElulR1Gjx/6MYXw1p1XFQaOA5ifWQca34OSmIHtivnFEA\n0el0UK1WUS6XrZ1Kn/BZtFhA9y2ioWF/MNH48ssvGy2jW1XwNaVw4vHhCVC6jfbMzAwWFxcxNzeH\nmZkZKwVuNBrY2trC6uqqjTVLoQmIEokEnnzySQwGA3z0ox9FNpvFhQsXcOnSJVy4cMFyX9VqFXNz\nc1a1w5W0jJbJ3X/xi1/E9vY2stksLl68iGeffRbz8/MGUIrFIpLJpC2iYiknoz0tj6Q+MRrv9/uY\nm5vD5cuXsb6+bnaG3DzLj7kTJ0t6w6gzRPahsadQH6kLavNC+obPwrLcSdsia8L+KHIiDD2FxomK\nzjBVO/N+akk5yWhIiXI5cbjJl+5DodsB86hAljuWy2UrK2MFAatdiOTa7TZmZmZsw7BsNotKpYIb\nN26g3+/jypUrWFxcxPz8vHHeTI5p3f7W1pYlXdkvrMd++umnzfFEIhGrUeYh0+HiEiZn1TCGHLEm\nsIrFIorF4thRcOwzpWcmJaH093FFq1SA8VN/aOB0svEzwPQJ96iFfcr+1XUOuvpUP0ujT+Qflulx\nDIC0imoAACAASURBVPjc1GsCI+ZsGL2pswBglBHL+KgLpCi4pqJUKmF+ft4M487OztheNsCQ7iAV\nxPzWW2+9Be89zp07h6eeesrOlqBz1i0gmM8i58/5yQVQy8vLmJ2dxcLCAorFIhKJ4WH2Ozs7RqVS\nn3kMINvDNnEeagKTK4iZd2Ailnkrto1lvHxmpc04Zso4hFSbjqu+H0ZwGqFzjBhdUf/DeRRGEQfJ\niTL0AO4yPuSNdSIflpidJqQa7ty5Y3uCMHrgUn8AZtCcc4ZSGfYlEgnk83ksLi5idnbWFjjkcjlc\nuXIFTz/9tIV8d+7cwQsvvIDd3V0Ui0WcP3/e9qx///vfj6/92q+1U524d300GsW5c+dw5swZrK6u\n2iHl+Xweb7zxBnK5nK2A3djYwDd90zchGo1avbIuzuGBKkT0NDCsVlEqgYaIStrtdjE7O4tms4lM\nJoPz58+j3W5jbW0Ng8HAKiCI6ll+qiGoylERvY6VTpRJtI1uCBUazJOE6KlLNFI0GCzb5VgwoqKw\nDzlOOgf4E8rKyoqdhUq6g4fSp1IpWxNBUEE0zO0F6NQvXLgA773t6prL5XDp0iV4P1xkdePGDbz+\n+utYW1uzIgTu0/St3/qt+Jqv+Roz1jSaqVQK8/PzuHz5sgEaVt1UKhWLIInIn332WaRSKVv0xf5j\n4QOdmnPOigHa7badwUydrFarY2t0GK32esOzJRYWFtBqtQzZM1/IAhF1yGHuKTTm04CoJmR13Hht\nOmaCAQW91A2t5z8u4D0xhp4PT+6bCsLEKDCeoGIHh3XGoejkYK34YDCwcFX3m+fCJlIaVAiG3aQ1\nyBPm83n0ej3bRhgY1hVzy9aFhQU8++yzdm8OGvenYaml9/6uc0RjsRguXLiAixcvGvIiMmG/fP3X\nf70tn2YyjLQLAMsLEBXoHt3kVXU5vvKAXKXIPjpz5oxFEERm29vbuHLlCqLR4d4q5DeJUMJxmoTs\n9XUtVdNxVsSkSBfYP3hFkZFSINqGxyVE3QQV1G06KSJHSjjhJ1VrhLy+7k9DZ0I0SsSuB3R47+3g\nbqL5ZDKJmZkZzM3NWQ6HCUzdNrxcLptuK1jg6VmsmNPzUGmoSfnwWqR/+FwKOgCM5cAYydAIku9m\nH3OBF0EAE998n1GtllzmcjnMzc1ZlMOtTrjuhVE/I+PQyB/ElYf6S93WaEzHNUwCM3dHalIXlLF/\njqrbJ8bQ8yGpGFz4wQelcQurE44jDBcTiYSFZ5wIzMoTfXGikJtnNp9VLTT8nIxE/qRGeG2Wj5FT\nd25YSnrx4kUA49ubcgUiJ64aByY92TdUOD0ghdfSviI6odJxLxIaf36HToKOhMaJz8SVs/F43FZ4\n0mExWuB5nmrMHoaQnyS1xnHVUFgn3+NG9WFpHcePESsdl054ihr3kCJQw8H3qS9q8LSyhz9ErIwM\nMpkMyuUy5ubmDAQwKUyaQ+/rvbeFU+Ey/sXFxbFnoY5pVRQdHJ0OHYkmnPmbDiN09nwG9pOeikaq\nlfsMaUmionM6IZaT6jYSmiNiybUuDAsB5qSoVUEL23mQsI0KBFS3NWo+TsR6Ygw9MM7Rs/6VybZw\nEcy9Tl4aAYZ5AMaUhjXHNKQ0VplMBnNzc6Z4yqeyLVxswaXk5O4BGO0TZv81WuDqRSoaJyInFdtK\nRB2JRCxMpVLoAQlM4mj/KjqjceHnlA+m8SGKisViyGazyGazWF1dtWolOjNysFrh8DANrC6eCvVD\nn/dxG3lgHHUxUmSbaei5SAfAmAMGxiPYMAcR0lrKL6tBpHHVbZG5cR5Xl3KfGBow3kMrsXgdfo7G\nmMhX5zANv77OeaDPSDBEQ0awxdc5trqwbJJB1dwSo2+tENPvEQwppUYHxzlWr9cNYRO4TELwhxn7\nUEKaUccxBDFKTYZz+Ti6fSIMvXpZRaKkHYja+D6wnww6jnCbYi11U75T98ZgJ1PhGCZy4QhRDgdA\nURD3CiEqpkHV6okQoZAuUYSv3C4/T66z3+/bSTscdN18SZ9ZS7bImyrXDWBsNR4nBqMqXofbGRPd\n09hzWTzDXdZ1PyzR5FWI1EJDcFKomzDK0P5XozMJvet3QoMVomZSI5rA04iBusf9gkJUqyWO1Esa\nOeWOgf099Kk3vB8jY+osdVPBjc5zzjnOdxr1MMIJnTnpHIIh1WvaDYIBOoGQSmQkkMvlzLHoHk46\nTqRXOU5hdKVt47X1NY4ZnaXSNRSOG3VCKcn7kRNh6IF9zpGDqokHpRNC3pISJkVCYYeSs1O+UhF2\nJpOx7YJ3d3ctNCRXSYPOkFUVRpE9DSUVmcrOtlLZ9X2GspwEGpJ77w2ts70sIaMDIJID9hN4bAsn\nLie4UknsE4bX5AR1ZSbfJ/VDzlKTesx1ABhDfCFXruhEHcKkUFh5+5CfJqpXY6nc53F5zIclasSV\notFwHBg3GIqqJ010NfSMoMKoTA+24NjSEDOioF5yszotRdR8h+bHgLvHjfOLuqmInahf+4L3oV5y\nHqjO6XqDEM1q1E0QxTp+9ofqjoIB1Q9dQcvIB9inBzk2dJiaE9A5OsnuhOOm77OPw89z7rP94TqR\nezX6J8LQhzQIBz1E3fcrrVbLVntubm5auKj3HAyGmznx9CZdcJHP51EsFscmA7CvlOQ6+Uyh0tBJ\nKVVCRQ77A9jn+9UpaH8oZ6eTM0SQyg/rbpWDwcDqoOko+DltNxNbjFzy+bwlZlnexlJOJpfDcVUJ\nk1HTJKQpDpPwfuHvxyV6f63oYAJQjZgCnRDQhPMkpHMSiQTOnz+PSqVi60N4T+oIgLFTzgieSN3o\nCvSQKqFRVPSsDluBmCaDGS0TpesGeGEiUo88pCEN76GOnu1i1EvnpqCA5cXKdfNadCbUa51rITdO\nCmdaAUgIMPR9bc80/VCHqvfVOR1e96hyIgx9KFSScBP++0VmpFu++qu/Gi+++CJSqZRtgETlq9fr\ntq82t3glVTE7O2uJT05UhsEcfCoP0YpSLorSqKAazmvyk45BUYMubuI1lJPUMFCNPdsE7CtamHRV\nlEeHx2tpwpMhPpeqc30Ad8dkKR4d9SRl14gmFEVg/J/fPSyRxT4JedTHaehp9NSJUrd5WIeixml5\nhpAWCA0+AcSVK1dw69Yt2zOFpbRMTsbjcTtEpNFo2B5IPCQnLOVj3oVFCXo2AI0ldVlRMHl7pQ11\nTvAawL4jop6GFBb/1tyGAiR1DGqcdd8aHh8YXpvzIBodbqCmz86af1ag6RqCUBc5dkcFGdOQPiUE\nt6GTP8p8UHmwJ23fh2jjaXiInIkqw8l/XOn1hseHzc/P25JvALa3fLvdRj6ftxV6PL2Jq++4tzxD\n4ZBzmyRUOv1fFV+5SEV7WjutCEZDabaFA67oXtGQvq7cJXlI9gONuT6LOiNuW0sOPpfL2a6ZnEjV\nahWFQuGu8QzHGpi+EV3orCZRB2Ef83qhkT/OZHgYou2n89Mcke4xRAnpq2moHsAY2ux0OnZQCB07\ndZvAoVAowHtvJZfkpwuFAtLp9FgZ36T7hzRa+B6wv8oa2AdtBFO8NuePRqa8Ng0/K3KAfeSvfReK\nJui1RDG8h16P/3OVsJ4UpzkUzhvSPOEcDW3SJEcQtiHU7fD76hD156DoYJocOguccz/jnFt3zv2x\nvDbrnPsd59wbo98z8t5/55x70zn3unPuLxy1ITr5VTGILpkU1MmvijLJ400KdVOpFM6fP4/3vOc9\nllgslUq2ek8nXiKRwMbGhtX1s1ad7Uin04ZclPphQivkWZVv1OoUNfhEwZwsuokSFVjDOb2mhrm8\npyJJ3k9X9/H+tVrNQm9eh/dmNQ+TVaVSySYt21mr1ZDJZGyC0FkCdy+eYvtCY0U0ps5GkVFoAPlc\nIa+ptNVBk+FR6TbbGiY+iXgJYsKJPMnIT3JmGvWcPXsWly5dMl3lLquM7HRrAOpwJpMxHWc7tCJL\nNwgjl89aeI1GdAx1vNTRTYr0+D2N2glO+N0wl8HPhK+F1XmsbFIqiM/PeUjqhztoauUajb1G5fqj\nbdTIOhxDbVNIW2rbDkLsoaM4jhwF7nwEwF8MXvsBAM95768AeG70P5xzzwL4XgB/avSdn3DOHan8\nIkQq9OzA5M6xBzgGYmMS8vLly/j2b/92dLtdC1dpWHTJ82AwwPLysi2qaLfbZsxCJ6JClMzrKGLn\n5mfT0CwRCJOewD6vSwei6EgjID1+zHtviVWWYzLsjUQiY8k4KjknxTRjy+fo9/t24hDzE3Nzc6aw\nXPHIZzpMDkLr+v4kUSev1zniZPgIHoFua0hPQ0dEqHSHfj5EyuHzaLURsL/I7amnnsJ73/telEol\nQ+xq6PjdSCRiK65ZVTap0iVsV1jbrU6BkS/1a9RvY4BDx5i6R2eiek00z/nCRYS8LyMYPSmKRQTU\nfaWA1QBrVBu2iWOi20/oa5xHdM6c19OiSdVN/c2xU5AT9uskB6JO5IFSN9773wWwHbz8XQB+dvT3\nzwL4bnn9l7z3be/9NQBvAnjfURoSev9Q2cIqAB2coz6wVpPEYjE7dFgXIDm3X39Lbx+LxSzJGN47\ndEjhe5NkGhrj6+QDtZaWoagiGOUKqbxUFg2FeU9OGk0CE70omqOj0PZO4kEZIXGyk8+kITnIeIV9\npEb6ICeqiO+oMs3oP0rdnvZck/olpKL09UkOQI0AI1EuZgppM61QIkplAlavy2tOMnyMDNWITaJE\nJlFvIfDQZC31BsBYUlg/o1SVompG/+qsCITC9oZ9rH1J/Q6R+zQDHSLwg3R3ki5rdD5NZ8KI4F7k\nXpOxC977ldHfqwAWRn+fBfA5+dyt0Wt3iXPuQwA+BABLS0tjCcCwSoBh3TQK4KiSTqdRqVTshCeW\nAnJpNmtodZUrE1H5fN6UlGhbQ1IdABrPsG1hdYUaeSojN2bS8jEdcEXanIBUGGD8sGLyoZwkLCnV\nigJenzXD7HeOB68ZOlkuNtM9RAaDgaHH0MizHSEi4TWVbpkkOikmlWvyfbZ1mmM5gjxQ3V5cXLRn\nBTBG8wH7W2druasaeHXY05yEjg0RLTfWYyKWfcPvhWWFNOB01qF+8nsEGARHSqNoOxVkUBc0ctZo\nVxOo1HlGtlp4oDSJVvRo9ErHxHtoG/hMk/pRdVZ1jZU26mh4DZ13MvZj15mgG3c5Qh1LBVVKhWmf\n3QvYue9MlR/e9dgzynv/U977b/Tef6Nuq6veUZU9DG+Bw0P+KffF9evX8fzzzyOfz2NpaclOkFHk\nwow7tyTWiCOkMhQ1ALCNmtRQKmoKUZk+D7dxZSXAJMTBMJf74TM5rEaUVRaK3iKR/dI2RfW6gpa0\njCZ5AViCKplMWolmpVLB7u6uLaw6f/48dnZ2bN9ylcOU8ihjqEYtvLZGMuH794qCHpRu6+SdhPT4\nDIwktaxRDeYko6rcd7vdxttvv40XX3wRvV4P58+fH9v6QPMpAMYSsDRm/E2HGkZ6pPd0HUWIPoHx\nnR4jkYgtrmM5KaMFNeS8TywWs7yBRiV8ZoIWtlPXA/BzvC8AAyWUcHsRcvTsBy6sJAXZarXsfaVd\nNbfA3yGPHkZlKpNsHsdYt6/QxYzhuB/V9t2roV9zzi2NGrsEYH30+m0A5+Vz50avHSo0lJwM9GRE\nKMB40iIMaSeFxmHoVa1W0ev18OUvfxlvvvnmWCKSq03pwYnquY1Bv9/HmTNn7DNUeraLiEkHDsAY\negvbxusA43vPpFKpscqBEBHRKOh2yDT2vJaG3aRoFOmzXVQWIiYiPEUU/B6NAOuOgaFCciOodruN\ns2fP2utqfFXuBZEoAtR2KxJke5VDPSxSmCAPVLdDBKdGIHyGEEGH9Ej4HCF10mg0cO3aNTvUHYAt\nkNPadRosBQs0qIyIQvAyiX9WIKLUHnB3EpKvhQlXdcwatWoClPqq/aaRp5ZEalEDgQmAMUpHx0Mp\nGTo6Gnptp+YJ9HlCSkX7QHN90/SCf7Md6uSVslIKN8yTHEXu1dD/BoAPjv7+IICPy+vf65xLOuee\nBHAFwBeOe3F6Z12pFpb9HUVU2bz3tijizp07APa3RAD2F1ZwKX+j0UAqlTJKA9ivn2UHU3k4uHRK\nHEQqLO8Rtk35UyqnGl713OwDNQjsK72G8pb6nobdbBt5Ub2/0kh8j47POWf5jXQ6bUfAcZfAXq9n\nDnOSHBaBTXLW+lk1eBq5EGXqHt73Qd08FN2exPfqM9Coq6HUZw77LHyfRq5arSIajRplo3sVJRKJ\nMSfI7yvA0jFSvaeokdTSXH1d6+t5b406Q3Chz6zGXyNR1c2Q2iX4CCMfnftazklQQACke/Wo4afh\nBfb3qqIjUgATRvkq01gI7c9p80HBwaSo9ThA6VCO3jn3iwC+DcCcc+4WgH8I4McAfMw599cAXAfw\nPaOGveKc+xiALwPoAfjPvffH3sKQA6v7ySiyPaqE3tZ7j5WVFQwGww3Dms0mnHPGXVMJuH/L8vKy\nefNodLhnfblcHkMDOnAcCKII3pOGFRjn2TQvwc+EFIwaA10wxd9EPvraJHpDJ62WbdKR0YGFfDGf\nlXt7DwbD0sl8Pm/HFHLy8fmm1TmHwnseJfwMuX1Fvfyt/RFGWZPkUem2csP8n+1S3dYxD6Me/a4+\nn/7NwzMUDFCvWVPOk5TC3VeBff0NE7i8f7hoke3XJCp3ymQbVI+0/dofyp9PM2J8BmA/B6YgRecj\nKRzy/a1W6y6QxLnuvR9bnZxOp8fOatBIl85Cows6s4PQO4C7xl+dkfZxOPfVyIcO8CjzhnLojPTe\n/+Upb71/yud/FMCPHrkFE0Q9vfJz94LQQmMfjw/Px+QqO91bg7XkNHaRSMROtacihR2sA6sIABgP\ndycpAg29GjuNCHjNEN2GRkDRBZVOeXe+Fi42ITWmaxSIiBUh6XX4OSaLSUHxs1zVm8lk7uJGH4RM\nMtqctMyvhEmrafKodFsdpqJGNXphpMb2h4gvpEJ4fc4ZbiVN8KIgQukt5mvC6ELn2aRoalI0qcUB\navT4XojeNarRPgkTj+F7GtHpXjhhkUPoHPU+4XvqvPR51elpu3h9dV6hhHP+IDnoOmyzGvl7tYMn\nZgsE3VJUO1IXlWgoOsk7hsJrUbm5SOXMmTNIp9N22g7PyqzVaqjX6+j3+7bXerlcNuOhuwLykAMA\nY4nLEI2FxjmsaqHyEWUNBgNbvq6KEolEJhpOVgupQ9RSNU4OXlONciQSGTtGTtEwkT8dIY8xZGkc\nK5ToPLhvEABbMs77KYJUOWqEFobFSjGokef20Lx3mFB+nKLGXJG0th8YBwc0ckp1THIK/JvH4um+\nL9yegsdnck5x+w7NEWl0oTkd7evQKGuuiWBCgQDvqVGCOhvOT57ZAMAcE7cPZkk0jZ46JgUqakMA\nmD7ofbVMlAULdEKTjK5GRmG+6aiRKO89TXRsVV81SuV2DurcHiiifxSiaGdahxyXk+J3OLGi0agd\nPXbu3Dm85z3vwbVr1+xwAk4KYKj0xWLRFhExicvSzHw+PxYK6oEHRNLhIOhWAlTGaVlz59wY3x+i\npPCz7MNJ4b+WnDGk1XIxTip+Vx2MKhnbTUqN0RA3SONimWKxOEaJee9tlfC0pNRhEnL7GqVp1YOi\nrpMkoQECMDapw2241ZDruIZ0nr7PMVxcXMSVK1fwpS99yc5WIJhReoKRV7VaNUOrOse5oKhf9Wsw\nGFi+hv/TefEavF4IzMJ6fDoWnTtE0wqGwmg6dHY8H1edEPtG7wfAaCyuFFZgGY1GTXeV+mOfsT2k\nQIH9EmR1xuwXlWn0DO0f5yTbPs3xKNg5ipwIQ09RJQmFA3ac0CUMM7kCdDAY4Mknn8S3fMu34LOf\n/ayVM/KkqVKpNEaF0JhR+bQemL+j0aghCK33DQdDjX0YvoelZqrsXOk3qc/CtmhfUlFp7DUBC2As\nV6FVPby/Ju74PyMLhs8cs0QigatXr9qEi8VimJubO9CBH0Wm6QMwbvRDiuskiIIYji+jDfa3luUB\n+3THJIoD2O8PzYsweimXy3j66afRarWwvb09tn6CY6T5ATXWNIYaHfI3DRvbRMcV0oKqWzSwej0+\nJ7l0BRN+xJfrAT1E4ao/IY3KNjQajbEtQ2Kx2NhmZtRrAgPOC/YDy5HpeJUmGgz2T6JjW1iQwP4L\nI86w/0KdCPVEx1wriKg7IYXzjkP0wL7SEkmEojzgUUUTPDRyXBzlvbfTmQBgc3PzrtKvWCyGer1u\nKw0jkf3jyoD9CdfpdIwb1byCKiknmDqCkLckZcK26+IPljxO6pcQ5ajB46lVaqzV+agiRyIRCxE1\nwgmjBu+9hbwAzAk1m03k83mUy2VsbW1hb28PAGzXz0nt18TWQc5AJ4v2IysmtF78JIk6Ho6vJmPD\nxLJ+ZhK3z2sCkyNhLZvkeayVSsWoGho8zVHxoBE1yopM+QwhYqfxUbDCz2jJoxp6RfNqrJWKoSjY\nUZSv4EbppEl6xFwE13pQFKApomYFF5+bczgEYLwGvzctMg+dEb+vY6nX5nOHaF4/F0YER5ETYehD\njkrRrk4CRQtUmjCcn3TdsDyMdd9c0UlU0Ww2kc1mUa/X7eDkarVqfDSRhpYU8jX9IWcZKrgqq04A\nPh95Td3MjZNJ98Cnomj/KLLWaISnXbEduVzOUB5LWLkvDdum4bue6ck+YwWShpq8ZywWw40bN9Bs\nNpHJZLCzs4NSqXTXOOg4hmgnFDVS+hkaeqJjLU/lhLqfSOJBiuZLwglLA69jq6W8dLhKg+hEV66b\nRpx73GjJKQA7MwAAarWaHUavBjhMbirtpqc6Kd2nhkqjQ4IIjVa0IIBARb+rFJzmpqg/PB9B6U+2\nS0UXh7E/dUdc9r1G0tqPfI+naPX7fTQaDesf55ztfaXtCw03cHcxxkFULPuUAEYjKZ1rx5ETYegP\nkjA5cb+iBpEhLbCvcOqtaRBDw8I26Zmwys/xN42gHtmmDiFEdYrmQq+uk1yTdTrhp3l3DVv1ObSi\nQA0I0Xl4Df2biWNOHIbcwHBPfzoJPdpukqG/FwmNnIa5h/XF45BJ+YkQyYafVzloXBXFKuWgCV7e\nL4xu9ag8jrtGm2xziGYVdClqD50ZdUx5c22P6p4+p0bW2ndhBKBzTxG6Pq/qtOrfpLnEvtNra5So\n9PFxEfVRJKR+VL9DgKB24Shyogy9PgQ7mF5Yw9Tj0DcqsVjMKIdUKoW1tTVbSk2UwMEeDIanL2lo\nS5TLa/GMV06s8GDmwWBgu0ryukz8qvfnICqKY8hIo8x7asiq6EgnRkgFkJdkGzTBpuhE+XyOAw/H\n0DHSpeM05PH4/sHqrLOv1+tYXFy0hTpH1YFQ9Jm0rVzEksvlxvZSV905CQZfUbEm85QHDg1YaKgm\n/U3RSc/IplKpoFarjaFpnTvVahXOOUvMkiPXaFGvTx3S+0WjUVvrQspFqULVa6UzVecIgjRCCNGw\n2oNw7xlgnO7l8/M+nJMsSlB6qtFojOklnyMejyOXy1kbSNd6P9ymmfMjl8vddTZFOCaqA5RJgFX7\ninpN+k139dQVvseRE2PoVYGV2uDgTOKtjiucCJlMBjMzM2NLivk+HQsNcqfTseMD1UDSaXBxVIii\nlM/nhl9cxtxut7G8vGyTh8+tpWIaZoYTQVGXog2dEAz5SbnQaVB0iXkymbQQX8/S5SRRdM9npwPj\n55WeIWJcWFgwqki3fz6uqFIrguSk1J+QA9c+elwSJjfpTHVl9aRk3SSOlu/r59X5ch8iRllE7fw+\n70vqjsZEnTsdkBpn/tY56pyzPZ1Infz/1L1ZjKTZdd/5/yJyiX3JyMjKzNqr2NXuTd1NgU0TtGRT\nehAlw6bHgG3Ow2gGY0jzYMgYwA9eXsbAQIAfPDZsDDCABEseA2N5DIyAEWQZkiyQpse2SDYpNtms\nUld1dVdVZuUW+5oZkcs3D1m/kyduRVZnNXspXqCQWZERX3zfveee8z//s1y/J5Bprum9VY+YPfXD\ntcPvDKkdZJVBTI09Es4jnjl/I93X6xt6SAFcSK7wihXZ94AoVLqnefmMaR6eX2OujXJH0XtD5eX7\nLOOZUvTS4+lDXnGFG+JpBzw7OfU+AEwamt98lPQXi0X77uFwaMifNEMUMhF+FMu0U+iJCXQ6Hcvr\nR+iSyaShf3LBPZKSNLEBmS/f5wY+E8PiNwnXZwOOx2N1u131ej1rG0vlZCKRMOUdCpMPcHEsHVxo\nuVxWs9nUhQsXTLH8KMY5/F5pkrLxSp57wsB+2gpeetxDmUY3ecU9DamHn/U0jHTynNQv4N14bh5F\n6+tSstmsNTYj6wxkjhLx8uO/E/RPoHI4HJrMcvwm3iiKE64bkEQsy7dRgE7kmVhP3sf38714SCjG\nROLkrIXBYGC1MoPBwOYREOa9Jo+oQ1DH86Pg6fPEfYVUSkirnKbbWBf/Hu+JeorV078fBtU/M4o+\nHB6BYOGZHB99f1rel8BiMpm0wxmkYwXVaDSs94UkO1X+6OjIjmfzG8GjCFK7Dg8P1Wg0lEyenEHJ\nfVJqPRqNtL29rTiOVS6X7VQbj6B8cRb3A9r3ri+GgE3jA014CB4psRE6nY4p+lqtpmQyaYFn6Ji9\nvT3r4Md3+V7nMzMzGg6HtgkzmYz6/b5WV1dNGH1hzGkK/6xxGL9BvKLnpy/nDzn7T2uwPh6t+dgM\nKaohNcVn/f/9NaXH5w0jz77BIM/Nzandbtvr0jHoGQ6Hdl8kFeAV+rXCAHhenwAuSpb3YfAPDg6s\n5oSirSiKLPMNo4yc42HiZfpsMmSMefNcup+DTCaj3d1ddbtd7e/vq9FoWMfMvb09a21ADGo0Gk2c\nnYyCh5L1mX4ga8BSmE10mnz7e52m6L2C9+vsKRzfofZpkTzjmVH0oVCHGyIUfn4P3aInjYWFhQmF\n/MUvflHf+MY3dOfOHR0dnZzqVCgUtLOzY4qYLAb4TEkTiAy01Ol01Gg0VCqVTJh8W9Nut2tGjRCH\n5QAAIABJREFUJpE4zibY2NjQxsaGUqmUlpaWVKlUND8/PzEfPnskRAtUts7Pz9tmwUOJopMiF5Ru\nr9dTr9fTzs6OhsOhKflOp2MZOhyQTtO3ZrM5sQnm5+e1uLg4kd88Ho+1vLysCxcu2Ob3G+U0JX/W\ntQuDUxiy0LX1qOdZoG2kxxuHgdTYwJ639zy55+wZIXcvndB81ESk02m9+OKLunr1qt555x2lUik7\nCzWZTBrdUiqVzKhns9mJewvjBJ1Ox4CPz3KCmun3+4a4yXYZDofa2tpSOp3W6uqqneYGMka2ffV0\nWL3r8/zxkFGwzB0y2Gq1VKvVVKvVDHBxjSiKjFOHEhmPx+r1epKO9zN9bkql0mOZSsvLy1pZWVG/\n35/IGvIKnvXwP70xCLOZeE/oUXgZDo8q9UzHjz2iD9FPiNpDpXFWZU9jrnQ6bYJ148YNra2tmUBl\ns9mJo9cWFhYmlIVHlHw3eeQEdNm4ZN1Ixyi82+1OeAygsH6/b5+HMoE7531hvrKfB//svsrVc/ak\ninY6HdXrdW1tbdl35/N5jcdjQzIoA6/Ih8OhpJNKSZ97z1heXtbFixe1ubn5oeoeThuhsvbCHrq1\n3hA8S8OjcB8LClG5z07yyjxU7F4OWHPvIVSrVV27dm1CtnO5nPVXp+0uCJrr+DnE+0WhEofCKHEK\nGoqeNeG1g4MDdTod2594rx7l+jRGvhPZBdVD/3m6huQHAAwFYltbW9a4kDYlfk7ZqzwbPD9KlSBo\nKLeVSkXVatU+N83ghus9jfL0xjzk/3mPjxn4eKVX8NM++6TxzCj6cNL8ZvYuuQ/OeLR6loHAfOc7\n39FwOFS327VceLi3ubk5bWxsmDLOZrMTlhj0Lp0ENDlEnAwVUMPc3Jx2d3et/ByXr9vtajQaWfdH\nBKfZbOrhw4eqVCq6ePGiFhcXlclkTOGHBV2MZDI5weP7rAIEeTwea2NjQ7VaTZubm+bKz83N6eHD\nh1peXraMJApuyDzCZT88PFQ+n9f8/LzRUgRxU6mUzp8/r+XlZfV6PdXr9cdc22nrdFZD4NEtc+uR\nKqje0xNeMX6aA2XqY00+duOVf+iJYcB8brePXflnbLVaunXrliFvlLPvW7O7u2scNfn0KFEU+mg0\nmugBj6cKmo/j2IAA/Y5QvEdHR3rw4IEVGg4GA41GI3W7XSuma7fbKpfLdjA5a+q9HuTWn80gaYIm\n6na7Fhvb2NhQs9nU+vq6Op3OBIWXy+Ws2j2KIvMKaIFArjxVrqVSSbOzs0ZDpVIpVSoVO7PZxz2Y\nv2k/PcXq9ZkfGDX0CmuOd5HJZEzGvWxz/bPun2dG0YeWEeFBWfhI/LTPThveqrLA3/ve99Rut3V4\neKhsNqsrV67oBz/4gfGABJUKhYItDMgBBe7dxcPDQ7XbbTtonM2Xy+VULpfV6XS0vLysfD6vZrOp\npaUl9Xo9DQYD5fN5U/idTkfJZFLNZlPD4VD37t3Tiy++qEqlosXFRVP2Pnjk0QFZLfPz82q321YI\nBbrp9/va3NzU2traRFAun8/rypUrunjxorm5s7OzqlQqajabVmDz8OFD29zZbNbc/m63q4ODA124\ncGEiZZX1kyZpOJ8J8SQ+fhrS8SjYUzbQD74q02+2s6Z2flyDzQsaDZ/dP2towD1XzLXCzyETd+/e\nVbvdNn78/PnzmpubU6/XUzqdNtpuZWXFEGUmk1Eul7Pv88iRcxmOjo6Uz+cnZJuzCMrlsvWEyuVy\n6nQ6KhQKGo/HajQa9rzj8Vj1et3onAsXLqharapcLtuJZMSxeB5QOY3aSIWWjmnQVqtlRuDevXva\n2tqaoPiq1aqKxaJ55f5QHfj5YrGoVqtl9A4Fk77VcrVaVS6X03A4NEoKOfOK1/Pw04Kz096HbKBn\nAC+kDEOV8j2hHvyxVPTSZBvQ8O8f5KZM+0x47c3NTWUyGTMgKysrWlhYsBTC8XisSqViAVjQItkq\nuI97e3uW5QAlk8/n7X3ScSZKuVy2hSJYtLOzo5mZGS0sLKher9tnQFqgttFoZEaESl3cStCVdwFJ\nhZybm9NoNNJgMNDMzIy63a52d3fNmJRKJVWrVc3OzqpYLGo8Hmttbc367afTaa2vr9umbjab9h18\nbzabnciiyOfzRgv44PBZ1i0coZIPOU/WI5VKGYeJ5+dliN8/Cvroww6/NpImEDsAQno8oBd6Q7zm\naR1vMPf29lSv1w35JRIJLS4u6ty5c4ZMZ2ZmVCgUFMfHFdKgevh9HwBFERIDqlQq1kYAOoTPcx/d\nblf1et3y0AeDgeI4NjoTrhkvsNPpWCJDPp+3fH7Wn2w08t1Rrj45YDQaGSUpHcfXkM1cLqcoitRo\nNLS7u6tCoWB7EQ8KJE1qaLFYNNlCkdNZs9lsmufzJOoEQxVW6no0H36OeAfeqs+k86nTHjQ8TXzy\nmVH00ybtNA4r5CtDpXCakkgkEpbXjaCi3BqNhhqNhi0wSjeMlCOA0kkFKIeHYxgIiEHTtFot7e3t\nqVaraWtrS41GQ8vLy6rX69rd3dVnPvMZFYtFVSoVDYdDxXFsFAmChhJjs/HsCIh0kpUzGAzU7XbV\nbDZtE8RxrOXlZS0uLupP//RPde/ePUnSt771LZXLZfNu0um0dnd3Va/XtbS0ZN09M5nMRNbP7Oys\npVZyT7jRe3t7ymaztiGZP49uvFdymhxMM9SeSyWYyQZhY3zaVE04fA45/+eZAAsYR2+4wuwaT1P6\neeP6mUxG9XpdhULBsmMKhYIKhYLa7baOjo5UqVRMWc/Pz1s6LdQGaB7KBURJB1LuT5I6nY7W19d1\ncHCgzc1Nk+1KpaKdnR3Nzs7q+eeft8N6uOdsNmspsMiW995Bt/x+cHCgXC6n3d1dtdttDQYDNZtN\nNZtNdbtdzc/P6/Lly0qn09re3jaP+c6dOyb31WpV3W53whP0VBrULR4tlBExBwAUn0OWfWqoNNlw\nzXuWfu1CHQVl5elr6BsMMnslpP9+rBB9GFzw/Ptp/6TpR9M9SUkMh0MtLy+r1WrZgeAHBwe6cuWK\ncenQDlybVEKf4uk5T+kkP50Fw629ffu2oihSt9vV/fv3tb29rUajoRdeeEFf+9rXlMvl9Nprr+lL\nX/qSbty4oT/+4z82tLq5uWloqtvtqlQqqVgs6vDw0Fw6WjD4TApoqc3NTT18+FCHh4cqlUpaXl7W\n3t6ebt68aT+bzaZefvll3bx5U1/96lfV7Xb1R3/0RxqNRqpUKhqPxzp//rw9azqdtiwk+gKxUUGE\n3W7Xsi7CNZ227tM4Sy8TrB3yQNaGR/XTvIZp1/m0hqdg4KOZDzqn0nMGY+nzx30AVDo5/wDvEoVd\nKpWMciRb6tq1a8Zng9JB5DTqIwWSwjcyUphb/g7CJVvs6OhI9XpdOzs7Wl9fV7fb1eXLl/X9739f\nURTplVde0RtvvKFqtar79+9bk7tGo6H9/X2lUikNh0N1Oh3zouH5iV2hcJvNpgV8t7e3tbGxoWQy\nabRmKpXSW2+9Zd9DkkGn09Ebb7yhw8NDffe737WEjOXlZV26dEn5fN6y7aCwJBknn0qljLrBsw2P\nYvTel+fbfY68j5n4z3rdNzs7ax4JegeF7gEQ1GsYzH/SeGagz4dFYdM28ZM4ezYdZ5vGcazV1VWt\nrKyYgMMv+9xeSYYcub7Pb5VOXKx2u616va5araZut6uNjQ29+uqr+sIXvqBisah2u62vfOUrhlDL\n5bLy+bxu3Lih4XComZkZnTt3zhT5eDw25IWght4OgkTjpfX1dQ2HQ73wwgt67rnnNDt7fLLW9evX\nFUWRvvKVr+gv/+W/rM3NTUnS/fv39bnPfU4vv/yyce+DwUA7OzsTqA4l5RUoSoleK6VSyVDfk/Ln\nn2aEgu6rYMM1fhqX9uMeURRZARNxEVL3kENJExWmKHxywEntJQZE10nmluuBeqmBmJ+ftwC5JOOd\nyTgbjUaG3vf391WtVq02AnrTl/gfHR2p0+loY2NDg8FAg8FA9+/f1/PPP6+f+qmfUrlcVq/X05/9\ns392In/+hRde0KVLlyzjbXl52YL97LFms6lOp2Oe9uzsrJ37gHFKJpNqtVp68OCB4jjWlStXdOHC\nBaNkrl+/rlKppJ/8yZ/UCy+8oN3dXfNoX375ZV28eNEUMKmYpIP6g7+Jw/kCLc5ERvl7esXvQX7H\n+w1pR/+7Zyd8do1PDw45fu6HdXxSnMuPD9SuURT9RhRFO1EUve1e+4dRFD2Mouh7j/79gvvb34+i\n6N0oit6JoujnznQXejyVzE+ar35kY/tJCpG+t6x+ksgSKRaLJsSLi4sqlUr6uZ/7OVUqFS0tLRkt\n4I2Bd6PZoGxANnIURXY488OHD/Xw4UPdvn1b169f10//9E+rUqmoUqkon8/rzp07euONNyxTp1Kp\naGVlRZ///Oftmq+99ppee+01u59ut2tZCjwPuccs+tHRke7du6dWq6XPf/7zVr17eHion/7pn9Zn\nP/tZxXGsmzdv6p133rFA8blz59TtdlUoFHT58mWdP3/egrqSrIoSI4hSWlxcND6Uqkxykxmkz/lA\nLP98Bon/5wWfwZqFRSQe1fvNwT8fzPykZdun4/FcKGbua3Z21moYaFtA/IT2FLzuUWKYz46XlUgk\ntLKyopmZGVUqFX35y1/WpUuXrAcRSooCq1QqpVwuZ4F1MqoymYwVRsGlR1GkwWCgmzdv6tatW3rp\npZf0sz/7s6pUKiqVSsrn82q327pw4YJdAzD1Z/7Mn9HCwoJWV1f1/PPP6/nnnzeFFkWRAQToEALp\nyM7BwYE2NjbUarX0wgsvKJfLmbH40pe+pJdfflnpdFoPHjxQu93W6uqqJTOQfLG8vKyFhQWTXzx0\nqndnZmas/oXnIRaVTB5X/bLfwt4/PhDMHHNN/z6vo3xMxrc8wRD48wNCD8BnI37QOAt18y8l/e+S\n/lXw+j+N4/gf+xeiKHpR0lclvSRpVdJ/iKLoRvwhDggPHyq0htPef9o1GPDmWOzFxUVtb29rbm5O\nV65c0Ve/+lX93u/9nu7fv6/hcDjRzMxPLooGJcjGhd+Dn7x06ZKq1apSqZR2dnb06quvamVlRb/1\nW7+ljY0Njcdj/dW/+ld148YN3bp1S/V6XQ8ePDC3bX19XUtLS1peXjakDgLxgSQ8EcbGxobOnTun\nRqOhZrOpZDKpq1ev6vvf/77S6bSuX7+u//Jf/ovq9brm5+f18z//83rttdcsEF0sFtXv97WysmJU\nTTabnfBe/FygXMJxGi3zYQbrPq1Ayns3p9FEp4x/qU9AtlFS3kXnJyl9YQ69P4IvzKsPU2wxjqQS\nUqVcqVS0tbWlF198UX/tr/01/ef//J+NHmy327p+/bp1Hd3f37fALN6DdFyERAB+f39fvV5PMzMz\nunz5skqlkhYXF9Vut3Xt2jWl02n94R/+oX74wx/q4sWL+ot/8S/q4sWLajabWltbs7gQ8lQqlXT+\n/HnFcWzZLL5aFtqIJIPxeKyHDx/q/Pnz6nQ62traUj6f1/Lysn7wgx8onU7r6tWr5lHPz8/ri1/8\nol5++WXLDCuXyxoOh9aKnLgdXiv73su2T6lk/r0OCj1c1sYDV79nvXcapmr6nk0e3PJ+n2b7NJ7y\nWQ4H/0YURVfOeL2vSPo3cRyPJL0fRdG7kt6Q9F/PfEeSBRy8dcN19KmNfpymRLyyIU3M96QBETUa\nDV26dEm/8Au/oF//9V/X3NycZamELhaW1geUKLseDAZ2DCGZO3CRFCX9jb/xNzQej1UoFJTJZPT9\n73/fFpSueQjP7u6uBZLgWLPZrKEK7ouALYisXC5rbm5O1WpV2WxWu7u76vf7mp+f14svvqif+Imf\nUKPRMIWzs7NjWQdkSpBnjYfhUSR509VqVaVSaWqHytN486cdXsn7fz6W8mHooU9Ctrl371WA5kF6\nPksJQ4YHIJ0oDZ+iGrYgnpubU6lUUq1Ws0IoZAx0+7nPfU537twxjwtZwWgSQMSAJhIJLS0taTgc\nant7284KTiaTJru0V8jlclpeXtaXv/xl/fzP/7yy2azK5bLu3r1rngifpRnecDhUuVy2pn88B89G\nSiWGfTQaaWlpybh0vBboJklGVdI3fmZmxgK4s7OzlgVHuij7GCVMOmoymdTly5dtP3ojzFyFqZQM\nX7AYvu5/Mgj+ZjIZi795EBnumw9Dc/8owdhfiaLoFyW9KenvxHHcknRe0h+796w/eu2xEUXRL0v6\nZUlaXV2d+gVeuXoO+sy8VDAh8Mfb29sW6ECh0gTq9ddf1+XLl3Xr1i2jeDyi55+/R98CGCVM4cV4\nPFa1WrXTl2hoRkbN4uKi5RyTpkg2C88bRZHa7ba523wfhsY3L+N72cRU2RaLRUt3W1xcNC6XoBcK\nhkPAs9mser2ezZMPRiPwCCgbcpqn9VGNkMvk/76IiOGV5IccH5lsk7PulTTphZ6GiR4F+VjjkBuX\nJhtg+ToF9gfKwlOcKKVcLqfnn39eV69e1dtvv210hQ8Ses+Be/VZKV5WyuWyPS957qQewnmXy2Wj\nhwj0UpFLcR6eqk9xnJk5PtkNZUlwGuS9v79v7ULCPXdwcGCNA0HeZB8xJ2SEAeBIWUaWmHeABFlK\nGBtfqORRO8Pz9n7tpr2X4XULfw/XxFPS0tOBmw+r6P8PSf+rpPjRz/9N0v/4NBeI4/jXJP2aJL38\n8stx6JqA6n0vEB/thmN7dK3HNg3DTy4pSwsLC9aP22+q2dlZdbtdXb16Vbdu3TJBJPDB/Xh3igwH\nFDfvJTsBY1GpVKxYY2FhQdls1iz45uamDg4OrNil1+sZkpidnbUcYdxJ6BsCVXwnHkq1WrXcYZ6L\n947HY+XzeaXTaQtAU7kbRScVib1e77GAnA/8EXTm9bAg6pQ1f+w1v17TAqt+7TzSZBOEWT3+et5r\ne4rxkcr2K6+8ElNN6hvMgUThmMNW2X5jh3PiET7PKR0j4IWFBTv9yycfRNFxMdDq6qrefvtt+1zY\nH8knFrC/oFPYD5ImApMob2Q7k8locXHRgreHh4eWg47ixviRXEBmG899dHQ0cToWIGZxcVG1Ws0O\n9yavnvkDvIDaQfa+Bbc3bIAbSdbhkjXhd+YvfI05fJKnGgKQ8HfuA3nwLAb34anJkKL8KDn6x0Yc\nx9v8HkXRr0v63Uf/fSjponvrhUev/ciDBfpRsjjIRiiVSrbpoHM8Wr1y5YohF08NYIQY/gR56fHz\nLr2w+r4VBGpoLdDr9aybHot+dHTSjZDXWVyPKPz/QSMEcBAUPAOMJxk8PqDJ95GBgVGTThAk1Bmv\neQTC9Z+WnjlNyZ/23jBoG36fl42n5Ov5/Mcm2z4A7ZGe91T9unrw4p/NB/A8zYdXhlKLosjy0SVZ\nxgvX8EHCsPqWmA/7wssCitP3npdO2ldTFOXbjABEpMlWHl7WMDj+d49ioRS5bxoUYpQIevu54Ro+\ngApC97ENz7sDekIe3tdDeEU7zShPAx5+/fx7T0tI8J6qV+re4zrr+FCKPoqilTiONx/997+RRNbC\n70j611EU/RMdB6yek/Stp72+F3LphLPnFHbPjz/N6Pf7VgS1vLysO3fumJtJdWsmk9FLL72kP//n\n/7y+/e1vTywUQuKFGytMVJ8TqXDRR6ORdnZ2jCf31yNThuctFArmwu7u7prAgcg9hcUGwQBgRHyB\nE7QKQk7fHBQB6ZNw/V4AOWyFHG+/NqAbNjYbgIEgPi3FdppiZmP5TJwnKXnu8cPQNx+1bKNs/Lp7\nQ02xWbfbnaii9sYzRIXhpuda6XRaBwcHWlhY0Pb2toEY+tskk0m98sor+sIXvqBvfvObpvD4Lu/d\nSieHeXCfeMSkZNLmGlnCsIQZKdAurAmyiwGh/QAeNtfxwEWSUTzFYnECeLBHmGs8mlarpV6vNxEA\nl46NAHSTdNIV0wdKUf6ANe8ZeSbBGy0fUwllgBHKJPoj9FD5nmnr/2ECsh+o6KMo+i1Jf0HSYhRF\n65L+F0l/IYqi13Ts3t6T9D89uokfRlH0byXdlHQg6W/FHyLjJlTyCDPd5ryifZrhlQ9cNhVvBKUY\nv/iLv6h79+6ZS4nwe0VLkZRHIqCTKIomjJFXPmysYrE4kdnDGbUo8LBUm+AS88Gm8P13/IlB0kkg\nlXvERZRO0tc8Yvc0liSrGwgRJwYSL4Dgs1fAZ+Hsz+J+nobkQ2X+JFR1ynU/dtn2lGQUnZzdC4Jm\nLWg3ABXnEec01Mi1+Bvrg5KkJTDeI2udy+X0V/7KX9HOzs4Ep849hnLmG/fRS577QlaQQx8/SafT\n1m4hmUyabANuMH4cYs5a4t14WeVZSa3l+4lH4IHg0Ugnsk0xFJ6Gp7lQrt578bQaDc8AR34NmHe8\nYWkyvTL0zkIPmOH/H9JA3J//Xq8bP1JEH8fxfzvl5X/xhPf/qqRfPfMdaHqgAcH1qAJB8X/j82dB\nb94N2t/f1+Lioh48eGB8HtWcMzPHPUFeffVVy0Lhc97wcCCDD+z6bpPeSkua+N3/HYVICTyLTcGG\nz9KAm2cOCKiBoA4PD02o6dFBvj/tadkE3h1F8fhe5LjFeFFeCbE54/j4EArPX3qE7keo1JlXvtsL\nfSgLfJfnMf21vDI8LbshHJ+EbPv78DRbuOlZE59NxXN56uI0hSFNtsH1CrFYLFrBz+HhoZaWlnTj\nxo0JesNn3nh6DtlA4dK3HgWIwmVd/H2HCtL3offGRTqhPZFt2ohgpFD87BdAFOmgKHr2i58z7t/T\nT3w3c+T1CsaN5/egAj0VyrLf1+G6hArc02TsM97HfXqQFBqNadf8oPFMtEBgeNQYRrZBF6RJUar9\nQQ/MgpyGHBcWFlSr1YzS2d/fn+jY56+DEPR6PZVKJUMUuHa+D0i4IX1hCBvdPzcDdEF0n+FRuHRS\nYBHHsW1i6bipE9/h6Z1sNvtYFzxvINiofk7ZhOQXszFAOiF/GBrrD0Od+LkOB/c1TcGH73tWBnOD\nAvLP5Tcwyo0K42nl7ac9lzeErA99UrrdrtV4YETIlsKLk2TxIoCVR8vSyTF6PsUQT5IeMOxR7/36\n/3tlyvMgUx644RUnEgkLpuK58l7iA8ivr5QGZaNH8FqmZcN44+q5fO8lhRWw02QzZCGk6R130Wv8\n80VP3qiE/6bRNB87R/9xDM89IbQMMl0kWeYIAvskegAhehI9cP78eX3ve9/T+fPnLb+Yftkc1IDA\nUKEIZ+2DnD6IyuJ5RB8GYnjN821kBSDkeA3krJMRw6KT3YOr7OcS1E32j6829A3AoIxCHlM6CYDz\nLJTeR1FkgWLuh9iCf8Zpw3tEHun69Qpf99diHUOvYZqn8CwMntUDF15HPgALKFvaHnhD6j/nX/P8\nsOeME4mECoWC6vW6USuAGLKuQmAVetNeLqYFfkG8rCWKHjrm4OBgopDP99/3yhXKhmchdsBeYg+x\nv5ARaCAygqTJDp/+MJ0wZhRy3H4OeN1TNAwv29OAjlfK0wyCV/Le6whl5jR95XXjjx2iDyfFI18W\nDoUGKmAzfNBDf5Cyh8qgvwftijkwO7xP3EiEyH93KDyeQ+Xz0iQC8/nUHun7z4Di+enRCAFRSbaB\nJFnaJJ/3gTd/Lyjo8PUQPYcUwpNokWkKOnym08Y0JR9+1zRlH26AZ0nZM7zi8Dx8WDiFTIQGM6S2\nphlU5iuRSJgyJ82XIGq/37c+N9IJsgZ9h56Hp4TYk9LjZxfzDNKxkvWfC70wPBzumc95KgvKUDqp\nB0D5I9dhRlkos9A5oUL14Cvci97jCNkAf41QzsPrPY0inkZ3Tvv9w8r1M9HULOQFfVADFxHEOhwO\n1ev1LFLOQp92XenJXO1wONQrr7xiJyItLy9rdXXVDknwE8wmpLkY3S79wJ1FaPg9tNJUuYJsQN8Y\nHp8FQDGXVwBU4Xp+G5QTx7Flw3AtOE7P0WMU4AW9IiEe4oNoCC/37efZo5sn/fP8+bS/T1s/P6Yh\neP+3Z4m2kU43dtB5lN5H0XEVNAffeJpj2hx5xeVlFJqCDJqlpSWTkcXFRZNtCtxYU98gazweq9Pp\nWLdJFLNH157q4TrSMcDAkOCl8B0+w8d7dlEUmbeMrPo4lL8vgJ/fCz77TDrxRLl3r08kmUz7oi08\noaOjo4k++hg1T8N4sDNN2XsDFBrNabQj/0IPLtwT/lmedjwTiJ7hXR+fwkRRQyqVUqfT0dzcnPr9\nvp0/6du++ut4GiIM0PF+PIWFhQUNBgPt7u5aDKBer1thiCRTyCD5wWDwWGaNRxyhMIToxhs46RjF\nDAYDa7AELw4q4yARukji6bDxUB64x6lUyjajR3qgHD8PYYMmgrAgKx+IomTdU22+W9+T3M4wSyZc\nf77b8/zeVUZh+LXkebkX/7dnYfjn9vfpC3aoiKU1gD8QJKT+uCaKMpQvn9EzPz+vQqGgvb09NRoN\nHR0daXFxUTs7OxPIVZqsCwENg/B9YZyfd8AF7+EevUx4jxS6CsMCmCAn3tOgngL1sutlnu+L49g8\nfJC9pKko3X+vb5oGAPKxKAbGY1pq72lUjv8baz7NOHg5CX96g8g/f+2zKv1nQtGHD+j5NCw4yEeS\n9bAulUoTPPiT0J40nRZA6XFg+OHhofr9vhYWFpROp7W1tWVBVnJ0GQQ+CQ7Bf4cbkHvzCpdN4QNe\nvogJbwLhAb37CkK/ITx/OTs7a/nD4fPD6/v58Nk1Pijl084wBHg00wTvo0LTIXIJg1The7ynMM0z\n+LQHigaD5I07WVv0lN/b21On05noQePHNGXA+oRrgXxns1m1Wi07S7ZcLiuVSqnVaplC9xSidAKA\nQLsAGmQjvC/QaxRFj2WPUXOBgo7jeCLexN7xpzr59fbUJIbGB1z5fg+s4ngy0OmBCWnagDLAFF6F\np9W8gg7ReDjfIWXo90iI1j1VM814PClOEMrCWcYzoej98IspnfBs5AZTUdput7WwsGAoJ+lFAAAg\nAElEQVR5woww7c6PaW4WJ/FUKhX98Ic/VKlUsg1SKpXUbreNPvJFHLu7u5YlkUwmrUApdLe90geB\ngBYQfu6HZk3QI1QfcmLOwsKCFZ4g1HCtlINzIDPX9IEt6URpewPJXHjeFLTj0VMcx4byp/G4HzSe\nBmV7I8dm8HnaofCfhpKelRGm37GxZ2dnrRUGbYJ7vZ663a7VRJz2TMgXIMRXlSJvpCKitLkXTjMj\nN90H4ilMHI1GEy18UZJQkWS0SCeKnrbKvJ+1o9DKe4RQRAcHB3ZOqjdce3t75q3jTQDGJE2NM/j5\n5f3SSQWyR/M+1uD/eRqH+fLK2gNSSY/pK+/9niajnnXw9+uVfkjXTWMtzix/Z37nxzzCjeB/J7BE\nxzwQK61Nvft11o3uXeBE4rhrZKVS0f379w0FsYCeT/doDI4PofBVcuHg8BBQlecs/X17w3ZwcGBl\n5ChY3u83bRzH1loV48Xm9Aic68dxbK+D4n2DLAyR7zMCfbS7u3tqsPCjGP56IGDu2/9khCgqvMaz\nMqZxsXhfnC5FCiOVpvD1obt/2rxDs0CRgITJskGG/fms3nNDvr0R9fURvgaAe4miE37dx5pYF4+q\nvcyzF4bD4USRIO/DY0gkEubF8h2+GR/7wvP/yDbX5V5D7h/ggvzjUfG807h47ilE36etuVfap8kE\na3fa+/29fBDKP208M4reC8G0HG3+Rn/o8XisdrttC+VdM5+dMi3i7gcLORwOtbq6audtSjKXmmuC\nbsfjsfVn9+6gz0lHYdN/g2sSTKbnNt6DzwPGrez3+2bM/BmWPmXTP18URRP3TKuI4XCoXC43wV3y\nOQwlG4v59MJG3xSPFlkzr4z9fIPm/PfxM8ylDpVgSNGEQUPWjef3isVzoh41fdqDdQN5+nngGZEB\nlA492Kdt9BCF+nVIJBJmjPFYc7mcxZqQZT9XHlH6tGWUv/dGPQWDJ0FvG2QVWeN6oZwMBgPLbDvN\nuHtZwjMJG9sxHz6W4b1d9iQj9Lh9Dy1eZy543V83vFeG/97TDLGX8VDOw89Pe284ngbQPHPUDcNv\n0DiO7RQcrwQ7nY6170UApJPF9GiCa34QCr1x44bW1tYkyZAVm4KCDapMOREHLjU0MAy/OXyAi2dE\nyYKwCLz2+31DSOEBH3gdBND4ztFopHK5bAePS7Ke35VKRdIJ30/hDN6IF3g2KPUKvgugz6l+EmKZ\nNkLP4ixjmhHw6+pRp7/+0yCej2uEhpE5Q1aIPxUKBevl0m63Tb4pcmM9JD2mKPx1veFASR0cHNh5\nv/x/NBrZQR9Un4KkUWzIBwaWeBIKyfPYqVTKQAYKlCpaaCQAWb/ft8w5OHlfyevvH8OH8pubm7Om\nfMSomFuP1gE9YVbeNG49/JwHi/5ZpUkAESL50Ovi/eHf+V7W0lOS0+THXzPUZ2cdz6yiD1FYHMfG\n48VxbAHZZrNpKJ/0QS+M4WaYxnf5wck6nU7HhM73/fAc8dHRkVWNIlRsBo/gKDIClXhhTiQS5p6D\n8L3bjGHBk+A7cTu9wmQTx/FxW4JOp6Pd3V3lcjm1Wi0tLi6aV+CRYJhJgQcC5+s5VUl22EQ4hx+E\nnMP3P60i9gbTo5xpxjukfD7NEd6DR6zISiaTsQPrB4OBRqOR8fQ+y8obVk/D+RRHL+ueRyaZod1u\nSzrp98KYhiY9fYdRQPZ93yToFQ9EpMnaAPYSwCKKIjvQRtIEBYORIsFBknmaZJOxP3wDwNAI8Vwe\nsbNHPJXjqUvum73BnHDv0xR8+No0uQuNDK95UOI5e+7df0/4ubOOZ1LRhxkX0ol7CXcOb95qtawE\nGyFEyI6OJtM0GV7Zh5N1cHCgc+fO6Z133jHl6+kHDljIZDKGcn1/G3rC+AZnfA5kg1FgMX1NAClx\nzIGvIUAgfUbD3NycnSZ1cHCgVqtlXgGnWnU6HWWzWUNw8Ld8PwjPc5YIGJucvGjceG+U2JAfJHjT\n0PZZUH1oOKcJ+bOC4MPhQYaPqzD3zCON9aLomL9uNpsaDAZqNptGwSHbKLIwxuNTXD2NSEfTdDqt\nYrGou3fvTpxj65Uj9wmK5xzgMF7iqTjWh9fwBpBpqB1Pu/CTM5AJKPOew8NDu19qQnq9nsWtiF94\nSg/Pmr3DHBBX8vEm7p3/I9uehoUOYl4xqKFxDNeb4Y3mNLA57XOnUTV+74Tfc5bxzCj60JJJk0gN\nJQgipvNkt9s1F5feNPl83ipnQbAg6GkDQUcACoWCKpWKbt++PbGZstmsBSVxN7k3qvj8T+45TJ+K\n43iqK+hpHElWSIMRiePYGq9hSDKZjMUqcHMHg4G2trbsvFjmg02LImfDIoS40hynlkgkjHPFaLDR\nuHdPF/i15O9sLmmSgjktbhJSQtLjByeHMsK1w58fRNN9EsPLXYiYJU0oVta5UqnYOg4GA3U6HVtf\nup163tsbZZ+l42MBzGcul1Mul1O73dbe3p55ERjvaRk4ZOZAc4DQAQu8jlx7yhT0jLL21CAgxtNJ\ngCLmjMO44zi2wr2HDx8apXp0dGR0LijcG1F+4oFIMlDkET5Ggb0c0kbhmrJ2nlIJZc+//zR59J69\n91bD7wrH08r1M6Popw1vCX16nee0Dw8P1ev11Gw2J4KGZK34xk2nTaC3pnDtFy9eVDab1b//9/9e\nuVzOvIjxeGwHOvu8X8+7o/h4HeUJqsBQeMqFf94Ycd/FYlFbW1uW1tlqtcy74TBjf9LUw4cPtbW1\npXPnzqlSqdgmJIUvk8lMGFayh0BVfC8GASQFjdRutye4z1DZYgB+lHUPh0eL3HdowP06hkjr0xwe\n9Xo6wKNqYjek6zL3g8FAjUbD1kw6OeQentoHDv33ETz3MhVFka5fv65CoaCtrS3LzqKnEuuMd4FX\nyv0CbjBKyWTSjubzTdGQJ97jaSA8FO4Nz+Hg4MCqcZPJpJ1xTCbM3t6e6vW6arWacrmclpaWDIj5\n5AavdH0w1Rsk7pW/SSdGl9RnGAKyeJA1f+0wqcAPbwQ8cPH/D/eJNwr8X5osxvLffVaF/8wq+nBS\n/AOhQDnCjOyERCIxUa0afs7TC9NQof/eROK4vSteATRQuNiSJvpp+54yYcqU51ERfIQN5eQFYH5+\nXqPRSO12W71eTxcvXjRhpZag2+2aUTs8PO7ZU6vVdOHCBeVyOTsQgpS6EFmEwhr+DeEPK3A9mvGG\n1G+CD7vufj1YJ08bhP9O89SelTHNcKHwvXLiOXzdBsVEJAb4DK0nufEgbugGabJwi+6r9EMKY0wo\nfE91QGf4gC337jOyPPL38S3ADTQLB9YTdwJkkUTA84KqOYmNozg5eY2+99BaPmaBNwMI8nRtGMdj\nYPhYG79HQ5qK4Z89XHcP/nhvqOB9JtFpa4rcfJBsTRvPpKL3E++Vh+e1/ens4/FYtVrNXK6DgwOt\nrKzo6OhoAr1OU0jhoEhjNBqpUChoZWVFd+/eVTKZVLVaneDbPSoAWcFx45ryug/ohNlBCBNuJEaA\nTIxms2lCTOUsm7/b7arVatmzzczM6KWXXtLMzIwJazab1fLystFYvszbowKvvBncI+68/65pY1rc\n42mHR7/SSXW0pwX8xvMbSHq22h9Ij9NKzL1Xgh71U6yHfPs0Yl/og0zzGqjbo3sUPjwzdEShUNDi\n4qLefvttpVIpVatV+7skO5Uqm83amtLHSZLRLlF0cuwgRmBmZka9Xs8AkH9m8tsxLNCBnPvgCwnb\n7badZCUdezKVSsXOWRiNRspkMnYIuc8g4/n98ZzoBy8nnsZkLUIPSdIEfYrBYC5ChO4/FwIXXvM0\npgeE/D18zV/Ly/2PtaJneDcmtGQIcKlUMiUAp+nTCrH0nicP3SY/WYnESdVqvV7Xzs6OURah9ed7\n8/m89euQTvrzeI/CowNPeYTIjBxqqlt9oA7KZ21tTclkUi+//LJlH/lAaaPRMIrpM5/5jN2/Ryc8\nK9/r78sbWVAchiWVStnB6l5YpR+dsgnviZ+eAgu9Kb+R2MTT5OXTGigEf/8oIh/c8wpxWldU+uB0\nu12j2+iRMz8/bzQirTOg4eC2USjsm/X1ddVqNeu1w5yh5AhsUrNClSxAByXPZ6gTIZsmkUiYQsYL\noWgQOYVymZ2dtWM2qXYtlUq2rzjHeDweW8xibm5OKysrymQyyufzNs/e8/bywJwA0CRNtPJg+BRi\nHyAGgIXAzIMMvtNTaP5vXrYBKsiEBzIh5RUaCk/b/NhRNx5hSo/nTrNZCJIgcGz0o6Mj5XI5bW9v\nazQaaWtrS/1+X4uLiyaYPoDlvQQ/QOtra2v65//8n2s8HutLX/qSIQYWC4FMJBLqdDqWRzw7O6tu\nt6s4jg198z2+WyQbh+fyR8mxaWu1mqTjzbO9fXxm9XA41MbGhpaXly0XOZ1Oq9/vq1ar2d+q1ap6\nvZ4ePHigXC5n88rv3rX188BrcRxPFFOxoelM6F1wAoUhj8jvYSzC/y3kI9lQvN8bHTaCb/blPTUv\nN+Hvn+Zgs5Jd5ekOjKlfC+nkqEbeCz89Ho+1s7NjRXBzc3MqFotWDY1cETwPg9fpdFpvvfWWfuM3\nfkO9Xk8/8zM/MwFCQuVE+jJpx1BJ8PVRFGkwGJgn4jNW9vb2rPU3VdXIPMq21WpZsJ/kilKppHK5\nbMp5b29P29vbqtfrqlarKhaLxuf7FGPOSEYJIp+g9uFwOPH33d1dy/rBCCF/vo2DD/J6XSRNsgzh\neof8f1iDwnt999gQ6IQ8vN8rT2ImwnGWM2MvSvpXks5JiiX9WhzH/yyKogVJ/7ekKzo+W/Ovx3Hc\nevSZvy/pb0o6lPS34zj+/bPcTBg09dY4tFwU8/iDBSjQqNVq6na76vV6ljVAJSvX9wrEj/39fW1v\nb+s3f/M3jZrZ29sz5YxLzT+CkihQEBmL1uv1lEyeHEaMAGazWUNqYQtgNoV07EI/ePBA586dM3TD\n0X3b29vW76fZbGp///h4REm6c+eOJNnh0J1OR4VCwTh9ryhxmX1rXCodQY64kyAyUGJYjOKHRzyh\nYE5DKqcNaDCfPvckvnTauk4bn5Rshwrce6o+ThPKpE8nRcF2u131+33LtU8mkxOFVcy5Tw9EGc3N\nzenWrVv67d/+be3s7CiTyRjts7+/b72WQnqIZwDd44n2+32TbUnmVWYyGVOGNAFEuWPsBoOB9vb2\ntLOzo0qlYjKfSBznxdfrdZ07d84Ah3R8GlwURbp3754k6erVq6aQs9msXTufzxtSRsnjGaPQO53O\nRDqqN8R0jY3j+LH18oo7pBCnUTT+5zRaEwPpaxSedL2npWxM7s7wngNJfyeO4+9GUZSX9J0oiv5Q\n0v8g6Y/iOP5HURT9PUl/T9LfjaLoRUlflfSSpFVJ/yGKohvxGQ5SfhLHGlovn7bnK+vK5bIFavv9\nvlqtliEm3/zMHi4okZ6ZmdFv/uZvSpIZkvA99PIGceDiEjwCLVC1Cy3ihYV2xAcHB9rc3DT+nesf\nHR3p4cOHE5xrs9mUJJ07d876ctDvg+yHw8NDSz1LJpPqdrsTVBO59KVSaaIhnJ/7o6MjQzfJ5HGh\nDZwryBpFfxaaBCMx7fWzKHvm2VdAcx+nff6MPP3HLtseqYcIL3T9+elRPymVrBNB2l6vZ6gd7hmE\n7eXMF/l1u139/u//vlqtltE4VHjzfhCyP7WJ85RR4qPRyKq2ATi+shSAhAzjbZO1dnR0pFqtZn2f\n9vb21O/3lUgcn4pFkLZUKpnn7M9RwCuAZqEAzPPt3ltG7gEweKQ+ZdRTfqRmI3eeZvOMA2s6TfFy\nHyFtw/Cf4x6ngaJQXqYZi7OMsxwOvilp89HvvSiKbkk6L+krkv7Co7f9n5K+LunvPnr938RxPJL0\nfhRF70p6Q9J/PcsNeVrhSSN8WJAeQoXwoRBbrdZjh4RMGxy4sLq6qna7rf39fasulU6QDYJGoIgN\nzcYhS6JQKCidTht36Z9zOBxanjAKlW6VVKTi2oE+0um0SqWSJFnHTPqXHx0daXNzc6LpE9/pC7JA\nT2HMwSsdFKlXmKBPlARG7DRF/yRl+7TCGm6mj4KS+SRkm43sM1dCVOYVAu/3yh7Uh9xJJ+cFHBwc\nWE8kT3eyh1in8Xis7e1tdbtd5fN5AxPkpqPQWEtPM6JgE4mEKfperzdxoDgKGRTtG6b5dsuAE/al\nb3+cSqUsrRMP/ODgwFIx+/2+ZmZmLJsM+fIek48DQOt5GiQMeJJAgbL3xtgra+5Rmp6+O81on3V4\neQgBbfjdnuF4mj3wVBx9FEVXJL0u6ZuSzj3aKJK0pWP3VzreKH/sPrb+6LXwWr8s6ZclaWVlZYK3\nDHlz6SQ1koWa9h5QLXm6UCiDwUD1el3r6+uGpH3mg3Qykffv31epVDKhSiQSajQaWlpaUrfb1cLC\nwsRC4mqSwy/JuEA4fe6ZQ02iKFKj0dDs7Kx2dnaUTqe1u7ur+/fvG/Kt1Woql8vmdh8cHKhUKqlU\nKlmGQq/X08LCggWgRqORHViBsZifn9f+/r6azaYhAoQ0k8lYNkKxWFSn07F5jqJIw+HQjBZzhAs+\njQYLx7Rgd7he3jPzGwx6wKN3rhkGxRgh+nma8XHJ9urqqskZWR48O2jSK/2QrkTOkW0UPjSgj81w\nHCZIlvmfmZmxwsJEIjHRBqNWqymVSml1dVXSSRsCSSZTw+HwMeSaSqVMfjA60EOtVstAFoid5AKU\nsG9QJkmlUknZbFbFYtEoJ+hLFH4ymTTun0CvJLs2soARIsZBMgb3KMkMCGDGe86ef2fuCchKjwdZ\nQ8oNA+HfF16b98MIIOMhGJxG3/h9fFY5P7Oij6IoJ+n/kfQ/x3HcDaxOHEXRU+2sOI5/TdKvSdLL\nL7/8gZ+dpiz8a/4ADx/FJoOgXC5rc3PTBI0BzylJzWZzIrqOy9ZqtdRqtSxFkWo+/l4oFCai9RSf\n4BqiiAm6djod3b17VwcHB7py5Yqlb87NzalQKBiawxMg33l1ddWEh0wLKB8qXn3uNYEolCP98xHY\ng4MDNRoNpVIpC/b6fvMIYRRF1kVzbm5OnU5H0pOV/I8y2Dw+2ybMTPFrxAgNxlN838cu26fFn/zG\nDxWHNHnYtSTj4qPo5ICPZrOpTCYzkc1DEHNubk57e3sTRW9eSTSbTRWLRa2urpon6L8PKhLDQAaM\nL67zacL1el03b960XvpkaPmmfHEcW+95rk+bZuJBYc0AgVZoF+pbmAfOY8C7wNv2GTg+wIoh5LN4\nJDxrKFc+H9+v4zQ+3QORaYac/egzsfx1ws/4++CnNyJnGWdS9FEUzep4I/xfcRz/9qOXt6MoWonj\neDOKohVJO49efyjpovv4hUevnXk8CSHyNxZsGq+fSCSMY0RZhpkaoas8Ho8N9eI6cy/1el2bm5u6\ncuWKRftZHGiiXq9nGxBjcnBwMLExa7Waksmk9TG5fPmy2u22KpWKstmsut2uisWiIehz546B5OHh\noarVqj0D9092T7FYtKyI3d1da4Ocz+f14MED47d9oQruMPwo6ZvwsGwchm+vHK4F42kV7GmDNeG+\nffCYzej/8d0f5vs/CdlGNsOiGL9h/cYG2WHQwmeLokiZTEaZTMa4ed92wBcGQtUh2xzDCQggaQED\n4TNMqAD3SpTro+QBG4PBwEDRaDTS0tKS9vb27BoHBwem6Pf29lStVu17oEOJtSGXxJ4WFhYs3tTr\n9ay//tbWlqIomkiThLqBGZiZmbF5Gg6HlsjAfHPv3W53ojWCT09l+DjbNIDh1wdPx9fQeGoGBR/G\nnUJab5p++zByfpasm0jSv5B0K47jf+L+9DuS/ntJ/+jRz//Xvf6voyj6JzoOWD0n6VtPc1Oncb6e\n0+QfD40L5hcBRBq2BsZI8LlEImGBLdAjRR2JREL9fl9bW1uWowzyIGef7wBh5nK5iY6VtCjw/F8y\nmbS2BpVKRd1u1/jQg4MD5XI55fN58xJ8n/j5+XkVi0Xl83kzMFQHk16HwBKc9nw6z8t1EWyeG04X\nvtUrGkrVQyUPJXCWdTzL+sNL0yrXN64L6ZwPa2A+Cdn2yH3afISy7BV0SLVxHQ92PPUIxYEx5m+g\neYwngXQoPoAHXWCJ74Dcff69l4lMJmMerJetRCKh7e1t49P9XEDZUMgIApdOFCnGgUpdAqncNwOZ\nQJminH1LBQwgQMcXVfr18R76NGSPQWI9poFRb8D5f5j663PlkW9k2gMBTwPxWX+dab8/aZwF0X9R\n0n8n6QdRFH3v0Wv/QMeb4N9GUfQ3Jd2X9NcfPeQPoyj6t5Ju6jir4W/FZ8i48daOifKWzaN3vyH8\nZ5hYuE/exyL5BmfSSRUgri19PKSTcm/ug+wGBFGSZSuQgnh0dHz2bKfTMUNBPICeNAhWuVy2Ht8g\neLJwyHh599137Vl2d3etOEySstmsZmZmVCgU1Gq11O12zYUmKAxFRU42n8U78IE4ag7gaJm/VCql\ndrttG4B8f+YKQZwWePVCOC2AxeteUbORZmZmjEpA2ZMJ4RGvN+Ae5U9DwlPGJyLbbFzu3Vdu+hRK\nr9TZ+NMCgh7Q8M+3HPCGmzRGKlG5PmibYC70BYpeOjkfmHqQZDJpRoPYD1SDP2yEAiaPqunLRJwC\nipCUS9YXZM9PkiP8s8LJeySMvJRKJdtHNPWDm4eTh+6Zn5+3ZAjui6JEPAXppDmfp2v88MkjHox6\nIOLvH4ONB8Nz4/2HOo3rhR6s//lB4yxZN/+fpNPMxs+e8plflfSrZ7qDj3h4AzAt0CdNFgeFVtwv\nFMJK2Xa/3zcO/eDgwAQok8nYqVO7u7smfAgPSJz7wYAgCHgT9B3hmMSFhYWJvid+02McoIkQokQi\nMYFaeB+pntlsVvl83hQJiILNRxYRAkkBF/Pi3dknZdU87ZqFVJqvGPygWEAIDk77Wzg+Cdn2QIUR\nKgqPGv39h2gQ4xb+TTpB7z7+QqYVn/ffi8HhH6gckIB3ixxRaMRAUWNAuH9iTSB/FDmN8JAzaJwQ\nvfrP8P8QfIDu2Q+AlYWFBQMHeCw8N9cCtMXxSerpo3U1xe4BA/LoZd57YcjnNBqRPRRSNz6dMpRv\nL8d8LqTt/N/POp6ZytgPGuFETJsEBgvrLSOuEqcreR6Olry++tYrTPjvtbU1VavViUXi/f1+3wKd\nnveHRkG5g7Sp8iODJZVKqdvtamtry86vpVAEZZ7NZi07wSM56eSAY9JI4UzZEPv7+zp37pyuXLli\nzzs7O2udOXu9niEyj949V89z8rsfPwJ9MvGT+wLl0CIXHprN6xXoNErEo/yzurcfx5imuL1c+gwP\nFEN4vyHq90rD15CgyFB+IHrQPgoxiiKj+EjdbbfbWlxctFbfyDygAnTpDT6ZaTyDry7FMFDIRPGi\n96rxdKXjdiV4wGTvsLbQkqBvkgG811oul83TJpBL1StZQxgLiqKYL3Lup8XomC8QPfce/vT6KeTw\nvZ7y3gcAzlfVs9bTDATX5+dpFNK08WOj6L2Lz0OGgVXpZGMhfLiU1WpVq6uriuPY0AWNkVBsWG4v\nYKQ44jKyKXK5nMrlsl0jnU6rVqtpYWHBBIuBUUFoUqmULl26pGq1qkajYYHT8XislZUVC2hx9N94\nPLb2rZyz6Q9FTiQS5nLPz89rcXHRkDqZPyCjmZkZy10G8XHMHEiOZ0XIoG4wHhyEwlrwjD/K2vq5\n8p7G/Py8HezCRvDDr1e4/iHt8WkMPz/w7l7h++wMH3vgfRhwr1QwdtCFlUpFy8vLOjo60tbWlj0/\ndB5zA++NEUcWOSWNZAB/XxgRKA0UIF6XpImDcjgRa2lpaSI9cnV1VZ1Ox76HqlxSOD2V44PJPohL\nEPbq1aumkKGH4jieaJ0cRZHVvwC2OIKQgi6802azaQVh0vF+48Qs7wlMAxg+fhK+xuvoJ4xyOp02\nmWbfkmzgZQavIzQmyM4Hebp+/Ngo+hDRS5pQ9tPeCzKM41gLCwu6ePGilTmDkqFa2Gg+iIoSLJVK\nqlarWlhYUK/XU7FYtMO2CUqR6VOr1axfuCQLNMVxbHnOS0tLun37tnq9nqrVqpWWg7CLxaK2t7fN\nrV5cXFS1WjWDAweayWSMCvIbs9frqVKpWNdD0A0tDVCm9DqnNw5/825sp9PR7OysdRJkg/kU1Y+K\nwpFOFAicLajT0zihPPjN5P8eBrQ+jYG8ohTxHLkvFAA0CXPP/U+jFCVZymEURapWq7bWBFE7nc5E\n5ohf//n5eTUaDV26dEnLy8vK5/NaWFiYoF5A+sSkfAzI94ChnQAKeWlpSffv39f9+/dVrVaNxsnn\n80okEpZGSTyB4j+fW09s6PDwcOJQe+49lUqp0WjYe5lPjvTkOdl70K3k9UOn0kaCqm/kDHli/0ky\ng+JTH71BCgf734MYT8PyD/CHUUdOPGV0mu57Gk/1mVT03nqFnJR38aXpRQUENKBsUqmUHZDN8Wxx\nHJsLGAowruPs7Kz+3J/7c8Y3bmxsaG9vT4uLi2q32yqVShqPx5ZVQ6ok2QJxfFzQEsexFhcXJzwF\nMmdSqZT9P5E4TmlLJBJaWlqyoB2bd2VlxRQF3+HniDnJ5/NW/EQlI6llxWLReNiFhQWdO3dOvV5P\na2trdtoQbvbR0ZFtKoJweDh+rU7LfvF84zRliyB7HtlvAu/eojD8BvBoKpQV/zP0Aj7JEXLjUCA+\na8hngXDPeJyeY2Z4anJ2dlbFYlEXLlywQ2nYK77Ax5+KBsD43Oc+p1Qqpb29PTWbTbXbbaMFoSgT\niYR5mBRs0W2y3W4rn89PZJnhJVarVfMgoCokGR3H+5DFpaWlCWPIGkN/AgBI4fQdMelB5dtkZDIZ\nyx4irfnw8NCMAHM8GAzsO/FWPSXqlanPeJo2fLDWK2efkUTBG8FXD2a83vIcv0fvoWyfdTyzin7a\nz7MMv0jSyeLQk53zU312i3ePsOoI63A41NbWluX3LiwsqF6vW4ZKInHcuAx+EzgAoS8AACAASURB\nVH6QSlmMRK/Xs43CqTm4h97K87ye6iHYi0LDU/GpbmHAVDrm9ofDoeL4uEAFvhQjBkrCfeQMXHLt\nycYhQIsROg0hn2WdwmCTDyKzwaGc2AQgH1D9k64NyuJ9nyY/z/DVpsyfT5tDAXD/eE2gRp+2ikyg\nFPh7Npu1lFzoN+nkfAUK6iQZVXh0dKR6vW4FfhQh+RbZhULBQAi0B16yJEsiQHklk0nzUnlWH3yc\nn5+31F1JFgPzXSS5RxA8MiHJOH7iUJLMSwCg+bYNyWTSABn0J/Puq37ZU76C1cuqDzhz3yHlOC14\njix66o35wDD5Zn2hgQhjkv56TzOeSUUvfXglL002kvJ8KIrE87bQHZIeC572+33rDUKFIUEqf9gD\nXD3o3rvbHoVS9UcQyafSsdD+s35hveD54iHca4SC/icgOt5L4QzCyYaDruH/vV5PkqzMHC8IBPVR\n0yCew/ZBR5SZzzHm9Wmcu38NFMR4FpS9v7+QbmT9pgVjPaL3KN2/5pFsODAM8M1QJvRZQjmD2Gdm\nZoyjZs35Xp9hglL14Eg68Y7xOAEyDBQkxo+CK9YWeQUs+fsmG4f58cDIZ8zwGX8v7E+yfghU86x+\njvDuParHAPPMIeCYBoBCEMM+5Pm8XE/j4ZH1UCaelraRnlFF/2EQfRgUkU6KoXyQJJk8bp3a6XQm\nhMEvBu/d29vT7du39YUvfMGuOTs7q3K5rPX1dV29elWHh8f9QkqlklKplAkRQopA+IyDcrmsfD5v\niJUUSB9UYgPx/GQB+dQzDFMcx4bAOV5xf3/fuPzxeKx2u635+XlzzUFtfH57e9tcW6oER6ORdb/E\nG/ENsE5bg2kjDNp6ZDtNufmNwObw15l2bf+3kOf+tEYYvOM1T+n4OAMjfM0rEl+9Kp0UBkrHbTyo\nmPbFcCE1ORwOde/ePb3yyitmJEDFFAam02k1m01DnD62I51Qb1x3OByqUCiYrHhPlFbfBCAJ1PKd\ntMXGkHQ6HQumInO0UaAGQDpJVOD5fJCWOBzpy9CZeK20EA8BBe9hvn0s0NOk4Zr5EYJND+T43adW\neoUeUpFhAJ+fP/YcvR9hICKc3GkBNz9hLKR3hd555x1D7iAklCyIhmKkl156yVBAqVTS7OyslpaW\n1Ov1rMlZMplUu91WFEVaXl42F9U3kfJVfShh+Hkf+JJkqWUeqXgqp91uG1K6c+eOrl27Zq4nAj8Y\nDIyjlGQNnpgnTvSp1WoWbJWOU0gp+kqn03rw4MFjGS8+m8Vvgg+idUKk7e8nXO9wU4VygJHmGqch\noQ+Dfj6O4T2V8HX/LNLkYeLw2aRHSid9nZAHSdbMbG1tzRQVMR4SEKA/6M+0vLxsKHZ+fl65XE7V\natUqZaVjRezbXpNxRbdM6cS7ZZ0KhcIEOoZi9AFn32oY+tEr08PDQzUaDUtyCIOWJE5IMkWNV9rp\ndBTHxy1C9vf3LaOm0WjYd6ZSKZN9AsIYLWgj5toHSr0CD4OjyJyPo0knRhpPwFfFehDjZd/rqzA+\nw99P826njWdG0fvNPG1jPsl6SpO9b5hQvyD7+/sqlUr6+te/bpY1RDykedEgKp1Oq16v68qVK8ZB\ngpRef/11fe1rX1O9Xte1a9dMEcPnE3QCydAhEm49k8loY2ND+XxerVZL2WzWlHG/39f8/LwJDYho\nZ2dHURSZcaAFw8bGhqWs4S2gFHyPbj4DP0kK3t7enobDoRk9xsbGhtbX17W3t6e3335b1WpVn//8\n581TYN2kyW6iCOdZgqChsIacpN80oQL3wcZQhhhPi3w+6hEaQoZH7N7j9MYQuWX9PMXgDR8xoLfe\nemtinaVjRe1bUksnyQooymQyaV1ZZ2dndf78eb399tvW6RXqpdFoGG+O8gOZEudBufsYTzabVblc\nNnCxv79vnDzrWK/XFUXHJ1oRdOW+6cR6/vx56wiLzPrsI9KfCWLXajXFcWzNCpnDfr+ve/fu6c6d\nOxazWlhY0I0bN1StVg0weVQfynnooYYUizdYkiaM9WneMAHqMMnA/84+8PvhLOOZUPTTkA7Dbwb+\nP234ySPNzPfvnp2d1Ztvvql33313gq+meCKRSExQKUw8gVbcQTIQEomEfuInfkIPHz7U5uamZmZm\ndP78eeVyucd662xubloHSkmm3Ml99t0v4Up9sBZUQgHU1taW8ec0qeLaxWLRDhdhU8LZ7+3tWa4/\nzzYcDrWysqJ33nnHuHjc5rfeestS1nZ3d7W5ualvf/vbevXVV+2ot2mK+oPWKlx7frK5QHlQXb4K\n2fOlPBdKNHR5P81sG4ZXzB6pM2/ESOCmvcIAjUuaSP0DqfP8o9FI29vbWltbM0oEcOGLmqB38FC7\n3a4qlYp5DtRoFItFXbt2TbVaTZubm5qdndXVq1etOVgUHScIdLtd1Wo1S91EllutlhYXF5VKpSyT\ni3XFa0ZGKPIjUFqv16140O8j6EnkIZPJKJvN2vz1ej3LeqNwa39/XwsLC2q32xPFh7VaTe+99569\n1m631W63bZ4weh4s0gQO+fbB9GnemqeMed17Wl7OPaL3hkE6SSbx75lGVX7QeCYUvTTJeYXR5qe5\nBgcsbG9v6+bNm5YSCWIlEMVG8AEq6dglZYGw/j4vniAT/OH58+f17W9/W4nE8YHG0DWkMpKNA0/O\ngqVSKT18+FBLS0tmkLD29BZBoBAMeoKAdA4Pjyts0+m0CTiFUfSsh++GPjo8PLRjB0lVk44NJWmn\ntVpNa2trajabqlQqmpk56WA4HA519+5dvf766xNBuCiKJqqCp9Ey07jyMCefOQ7P8PTemkc+3uWH\nPgBlel700xoe2XnKS3qca2fOPEWTzWYlHc9Jp9PRw4cPtbGxoc3NTW1tbWl3d9fOWt3Z2TE0iuGH\ngkin05ZdA0r3VdkUK9EGmPz1ra0tDQYDtVotU35etguFwmOdTdPptJ1d7Pvm8H35fN4OOeeakgxk\n7e/vm+HwPZ6iKDIPgX2CbGL0Go2GgZp6vW7gqN/vWwO3nZ0dNRoNlcvliThYo9FQOp22wizuif5O\n/N+jfW+8/Tg6OrL4F8/IvgC4YaQoXmOdQ8qGPQy/72MKZx3PjKL3wyt5HvqDHgrO7t69e/rGN76h\nt956y/rIowwKhYJx8/zks9LJCUpw29A0IVKEIwTtVioVtVotO0MT2obAFYhjb29PhULBBLTT6ejC\nhQtqNBo6OjoyrhCF7jlokBwpcAgwxqpYLJoXA0JEkLzbmUwmrYEb3Cd5yQjZwcGBISoCzChYjpGb\n5qp6jv5p6ZJp3D2KEA6YZ/FZRV7Re3TP/cKrPgvDc6/S8Xp4GkQ6CeJhqODIu92ubt26pbffflv3\n79/X+vq6ms2mxX5yuZy14ADESCfVsJJM5qFPMIh8h6SJeYZyIQUzDEiSjotyphEZxspTODyvpyai\nKLLrIu8ALW/88eYAX+wBPGu/5r1ez+hRYlU+IEwevefHWRdafJNyjEyiH3w2j4+p+OH3xLT1l056\n+qD0vez764ZxG2jMJ33HaeOZUfQoL3LMySDB+sGbe+tGytfa2pp+93d/V9vb23rnnXcmDlyQTiaJ\nz8zMzNh3eNQsnXgF0smxb/fv39eLL75orp7PtZWkF154QW+++abW19eVSqW0tLSkKDruoeErCn1u\nPRQKJ/yMx2M1Gg2VSiXrp42CR1iHw6E6nY7a7bb6/b4FdNjgBIULhYLlKvsmZIPBQJ1Ox9x20uka\njYbVANy9e9c8HuYcFAHH2O/39d577+nFF1+UJDOIBL3wKhhk+0iTRtWX5Hs+HgRFDAJ6grn3/DZr\nFqIen2Xi0/s+rYHsSTLlBrCQJiksf0Tkt7/9bX3zm99UvV7XrVu3VK/XJZ00l+P5aGuBrBHslGQc\nPvOzu7urdDptmTef+cxnJJ3sE5/LfvHiRfX7faMnc7mc4ji2+wORsvYg43PnzhltRMaXP8WMcyKG\nw6FVaEuyg8+z2ezE2a3ErjKZjLUxxphAX5IOTWwhmTxuBZ7JZLSzs2OncPlus8w5+7nT6WhjY2OC\nciLtGJ7dGzsMJQkL6BMAik8oACixv0H5XNMHcBk+Hdx7huzv05IfwvHMKPrDw0Ntbm5qbW1NURRp\naWlJS0tLKpVKyufzE8EHBLHT6ejrX/+6/t2/+3dqt9sTStuf5SqdlKCH3oK3migfn8kzOzuru3fv\nKpvNanV1deKwbe5ra2tLzz//vL7zne+YUPuGSxzwwIbgeQksSceo5cqVK6ZMUZaHh4fq9XqW5ZPP\n57WysmKHn5DG1m63FcexlpaWJtzBZDJpri3Pvb6+ruXlZVOg3W5Xa2tr5lGMRiOLNfB/j0bH47Fu\n375tqXe8B8Pq7525T6VSWl5e1srKitUT+PVgvr3nMBgMjNrBQPhsA37HSHguGq+KlLtPa4AyQeBR\ndNzGd3FxUSsrK5bDTpwId//u3bv6T//pP+lrX/ua1tbWJp4BNOopAZRQMpk0EOMpLhSj73MURZG2\ntrZUqVS0uLhoyBzlxfWuX7+u7373u2o2myoUCpYYgFGnFTIKDI+QzLXDw0OL6YDKu92u9U9CvtPp\ntB18f3R0ZCmUrVZLR0dHWlpaMvCEYUd+2fdU61LxOxwOVa/XVSwW9eDBA/se5pDnPTg4MPD0/vvv\nW4sFDJ/fl8zrzMxx+2WSIBYXFyfqaAAxeLrsQU8p7u/vP+bVSZMJBuzzULalj/iEqY97bGxs6Jd+\n6Zd0//59Q/Wkg7300kv6S3/pL+knf/InVa1WLQf+W9/6lv7gD/5ADx48mJhAj8b9CHlQ/5NMBZ9u\nyWIQ/EwmkxY8hS5ggRYXF3VwcKDnn39et2/fVrvdnji1ngZOe3t7FmgFEcVxbDQKeb2JRMK48+Fw\nqJ2d4wOOyuWyMpmMLl++PKH433vvPXuNnOFEImGIHM4XCub8+fO6f/++oT6Eplgs2mbmNZ8W5ucx\nlUqZB0PjK/4OMsdQSsdI7f3337cA4Orqqm2EMGiFAeJ7PYcZuq0+SOWLbZAjspc+rbG+vq5f+ZVf\n0f37960LJFXK169f10/91E/pjTfe0NWrV9Xv97Wzs6M333xT//E//kfdvXt3oj86su1TdVHiGDmA\nBNlVpGJCV8Jxo1Ru376tvb09ffnLXzaUSLUmsri0tKTnn39e77zzjh48eKBMJqNKpWJxKgKMqVTK\nUDxAh5x66JPZ2eNzkslw63Q61pspnU7r4sWLE62333vvPV27ds0yara3t5VIJFQsFtXtdieQLfQs\nNCoe9O7urpaWltRoNKyC2M+jrwcAuGxvb5vSRkbxLvw/aLV6va5Op6Nisahz585NHMkYZqERg0gk\nEhNy7mk9f1+so8/z99TuWcYzoeiHw6GlVXlaJJlM6ubNm3r33Xe1sLCgL37xi2q1WlpbW1Oj0TCF\n5luaSrIADYIqnd6/mQXzip73MZmS9P7775sAofz4iYKh5S9l4fl8XoVCwY5q29raUhzHKpVKWlpa\n0rVr13Tz5k3duHFDtVpNe3t7arfbFvXf3d01tHT58mUTRCgY+mWsrKxIkil3fzRaqVRSu922bAoM\nR6FQUCKR0Pr6ura2tvTcc89Zz3pcUN+1j8G6DAYDLS4uGveJQpFOyuL9YRcgI3qqdDodfeYzn5k4\nVzcsVvFGOET+PK93jUE8Z+FSP6mxu7urer0+0eKAjKc/+ZM/0e3bt/UHf/AHun79unZ3d9VsNi17\nBk8I993HJlgHZBx5oRjJ599nMhlLjcxkMup0OqpWq6rX65qbm9ODBw/04MED8wTxnumE2u12zTj5\nM5dB68PhUA8fPjTUzUHj29vbBo62t7fNyEPPdTod7e/v69q1a9bJcjweq16vq1KpqFgsmpfL8x8d\nHanb7arf7yuXyxnyzmaz6vV6Fms4PDy0ub9+/bpl1dCXh95PPosLDzuROO6UCVVLi4W9vT0z1sgl\nP4+OjtRoNIw6qlarFo9DNqWTalnAlwcwHsT4FFqfuUX2D+msIdVz2ngmFL23eN4K+vS6nZ0d/c7v\n/M6E0vEVgR6NYwA8YiRv3FtonwXBd/nUL18IMhqN9IMf/ECFQsHoC5ARqLVQKOjVV1/VN7/5TbsP\n2uwOBgOLOYB0qKj97ne/q3Q6bU3LOO1nNBoZf55MJtVqtXThwgV1Oh2tr6/rs5/9rLa3t7WwsGCu\nKG4vGTKVSsXQAAFh0teOjo5Uq9VULpeVTqf1/vvvS5pMDUNIMWBewXjOEpSBmwsHyvwx16xNvV7X\naDTSpUuXdO7cuQkeEnkgA8RXZYaVubzXN3hDyUFV+F4xn8ZA1jyqg8YYDAaGlCU9huAwVhg/lBJ0\nFoof+YJWYN5QamGvG4CAdLx37ty5o3K5bLUfuVzO0CY9ji5fvmwV34PBwAqj0um0pTqyB1G4Dx8+\ntEPviZtB89TrdbvGYDCw9iJkXO3u7honT/YLAdh+v29yS0ow8wZls76+bjROu902Wuzw8HCiKyqG\nE30BhUsGUxggZ/hMPElWtc5rFEYS7/LJCmHyAZ/xCp6/8RpGhdO9uL+zjGdC0UvTqyTDgTKexnuF\nyA2FEUa0fTobCtGndYaDxfRBSx9Ek056ZnOdc+fOWcoZVpdNQHl5u922vGQ27NramnGLeDeeFx+N\nRnrvvfd0/vx561u/u7urfD4/kWLmXXuEEPoIowU9Mh6P7bAJ7wX5TCOPnOEmuS8EH76ToCmveUTv\ns4d4jTxs6Ct4S2+kQcGsme9kiWILPQ+fJfJppleiJBje7Wd4IAJ688DFGwrv4bBOzKl/ThQBisuf\nrcrg84lEwg7dhof28Q8oStp1k85JczNQPoaBcwu4D9ab6yF7rBvpj9Ba3PN4PFa1WpUk84r9fCKL\nPjuGzxEoJuEAmefZ8OClE5rW08YYAa8v/Lz49WWN+IlHS0GXD5Zz3/5ZQrDk95tfd4/2qd7/yKib\nKIouSvpXks5JiiX9WhzH/yyKon8o6Zck1R699R/Ecfx7jz7z9yX9TUmHkv52HMe//0HfA2o5LW3I\nL4w02dqVz7t7NiH2SgZB9KXjDNB7OKABstmsms2mLl26ZPnI/t6wxkdHR3r99dfVbrf1p3/6p3by\nFLn0o9FItVpNtVpNhUJBzz33nPb39821vHTpkgVgoUSee+454+2Xl5dN4IbDoQWrJVkbhtnZWTUa\nDUNOo9FIq6urFijGU9jZ2VEyeVyl2+v1tLm5aZvaD+YTI0HxF4EkEDa8I2vFZgHJexRONkO9Xlez\n2VQul9NLL71k1xqPx8bLbm1tGfcsSQsLCxOnbfnAL4qJ7wgzgILn+kRkm2dmM3uqCsXi4xRRFJnC\n9e67l0n4Z/7hTcVxbHEg0gh3d3dN4bVaLcuCoqBufn7eKEOu65Env+fzeV2/fl2dTkfvv/++9Vqi\nFTYe4s7Ojsrlsq5cuWKKvlwuq1AoWBIBfPr58+cnDt4gT5/MuUqlol6vN+HdUzx47949HR0dpxb3\nej2jqGq1mgEqWnavr6+bQveZLKB0QANVxcR6+AyGiZRYD3z8fgFooZ+ow8GA+6wZ9jlFbqwdZzGQ\nXUQGURjHCkHEk8ZZEP2BpL8Tx/F3oyjKS/pOFEV/+Ohv/zSO43/s3xxF0YuSvirpJUmrkv5DFEU3\n4jMeEH6ahcLllyarYNkgPtXI8/IgHZAnC+AVM98bGhP/fq67vr6u69evW7ApmTxug4pLu7+/r3q9\nrsPDQy0vL1vAiHusVCrKZDJ68OCBLTpc/Be+8AXb9BSWgJ4IpNbrdZVKJS0uLlrq2Hg81s7OjtbW\n1qw/uCTrLy7JDjehCKxWq1nKG/nGu7u7lo/v0SL0lJ8f0JF0clKVD/x5Ws2nsaFE/LxSt3Dv3j0z\nYMwDXgqUlHQc08H1Xlxc1NLSkgX9yMris09S9PqEZNt7l6BvBggOw8f7QIEoBRAgGx7l5K95dHRk\naYugPS+Xfh9AgWAMDg+PK1R7vZ4uXLhg9+0P/mD+Z2dntby8bIaYxIRCoaAoirS+vm73Cyii/Qdg\ngDbJ+/v7llpJq2xiTQSPG42G1tfXVSwWlclk1Gw2rTBxbm5Oq6urajQaGg6HE7UlFETxt4WFBdvH\nGCn2FbKDbPomhFA9rIeni72MepaB65CNxt98Q8L4Ucqo94JJbkilUioWixY8JhDMvqK6+SOjbuI4\n3pS0+ej3XhRFtySdf8JHviLp38RxPJL0fhRF70p6Q9J/fcJ3TKAZ6cSt9NTGtMEEggjY2Fhtr1R8\nahmLA2pis6DMPL/sU9m63a7a7bad+ASi5H4p6PAuNt9BKtZwONS7776r3d1d/cmf/IkFU+/cuWOo\nyvOa6+vr6vV6unLliiqVilX5pVIpvfnmm3rttdc0Go30/vvv67Of/ayazaYajYYWFhbsOERy3/P5\nvO7cuaPl5WXNzMzYz4cPH5ri8IU1rAc85ng8nqi09cqaefB59yG1gmfg2ymT3dRqtR5LcSUPm+Hj\nJ5LMOyLAzRx75U7r5Sly97HL9jTwQjwBeQWs/P/tnVuMndd13//7zP1+JUe8X2RaFxuxLRiG4xYV\n0KJx7CBw+hK4QFoDTZA+BG3zaDcPfQj80AINkJcWsZMGfnAbG02q2o2hxhYCOAZkyRJtxxJpmZIp\ncjjkiMMZzgw595nz9eHMb5//WfzOcOiKnCF1FkDM4Xe+8337svbaa/3XZYOZY867Aw4+3m5r3oB5\nNrADcBxQEDi916VnI3cHOrAbwn5kZKThmEFvO1FZrDtP7Cq2o8goINbb26u2tjZdunRJw8PDWXBS\n+ntxcVHXrl3Tk08+mX0HbAg3b97Mwp9AAbRgIsSwZObm5rS8vKxr167l7NbDhw/nxEQUEAQ7MAkR\nY2k7Ooeza70Eg1ulWBWMuQeB8Bx4DyUT65S5Y36BJeN1PlertSqzREp53owXhdsN3RNGn1I6Kekj\nkl6S9A8k/ZuU0r+U9IpqmtFN1RbK9+1nV7Tz4pFUj5qQ7kyKcScWf3EMIlSa7W6eoCOVHxDguJs7\nIX2XZtMoikIXL17UU089lcvBEsHCs8fHxzO8QnXLixcvZpNvfX1dH/rQh/TjH/9YknT58uUGUxKs\n9NVXX9XTTz+dhfvBgwc1OTmpt956S0888UQWvG+//bYGBgZyvZKJiQlNT0+rr69PP//5z7O2cubM\nGZ09ezYndxTbEUAcUAJsw2JgPLB2pMZzLGFwGNNNS6773+iY5fkI/Wq1dggF8A0meuQT3whozzvv\nvJOrEXZ3d2t0dDRHiuwGo79fvO3OVRfgroU7H7P44VEvEQyP8xxXJNCAgQ0GBwdzvRfmDn8O6wW/\nDbw6Pz+vubk5VavVnNgk1Wvad3R05IiwmZkZjY+PZw0ePHp4eFgnTpzQT37yE924caNhviqVSi6h\nnVJqCFcmBn56elonTpzQ1latVMe1a9e0urqqxcVFHTt2TMPDw7p27VoW8NVqNfsXiFwjAAEljIge\neAmoC2XFFTPXmv1kKwQ88ijCJu4P8twN3knYKeTyijXhmbpbW/Us4UqlkrPpKdXc19fXkN1/N9q1\noE8p9Uv6S0m/XxTFYkrpv0r6Q9WwzT+U9J8l/at7eN7vSvpdqfE8TenOwvpxoYJ3ca+nSEft3yEd\nd2ohxJlAf7c7+ni/P2NyclJXrlzRk08+mSeM2hhoQIQ+Xr58OR9oPDk5qfb2dg0MDGhqakpPPvmk\nlpaWdPny5bzQsBqI1pmamtLp06c1NTWliYkJVSoVTUxMZG1sfX1d58+f19GjRzOEdO7cOW1tbWlw\ncFCnTp3KyTqbm5uam5vTwYMH9cEPfjDHqC8tLWX8HmZm4+EzGj7mKFop2ro7XSU1aD2+kUbfiEMZ\nm5ubDY5kn39fFNGh7uY0MA95AtxzF168r7yNYI2OPGLWGV/3UbHoEexlVi/99Y3Dhb/PGSGIQBZe\noIuwXY6UnJyc1IEDB/L7GEfPU5mYmNDU1JQ6Ojp04sSJHDqMxv7000/r1q1bmpqayto59e3Hx8fz\n9SNHjuTABawBlLiNjQ2dPXtWR44cycrO3NxczmwdGxvT1NSUzp8/n+HPQ4cO6amnnspjPT09ramp\nKQ0NDTVsai4jvNwJx3ri53F5ITX6ApkXBLxDk5IydEg2LBuJyyh3sLrvgL+8n8qflUolJ3ZJyvj+\n3WhX4QgppQ7VFsJXi6L4q20Ge6coiq2iKKqSvqyaCStJU5KO2c+Pbl9roKIovlQUxUeLovhomSCP\npr7UeD6sa4dRQ3eh4vgwzyhpS1OtLz5bqk3w1atXGybdww7LNLfh4eF83irmry8mSdkRNj8/35Ad\nOzg4qNHR0WzGes0eNkXwy97eXq2srGQoBGfU/Py8rl+/rv7+fg0ODmpsbCwfCE3EjkNUzrg+jm5u\n+vj5QnDT1C0zKAosvwftNfpbfA78e+cJ1xyxDFjAzeh+83ZMhGGhe8hchGFwcEt1mNF/72Pp64T7\nfb7cqvLxZpN3X0pbW1sOe/TyyGnbwU1fwK7ZoOAp+jQ+Pp6L4TGHCFGvZQPcRFkF3uPaNYoX9ywv\nL2csXlJWUhYWFvJ9Y2NjDTAR8x8dsUTt+DxEn0iEWniOy6Uy5cV53tfRTuS8zPi6tcc/0IZ3NWEq\n1Vr3Z5LOF0XxR3b90DbGKUn/TNJr25+/Iem/p5T+SDWH1RlJL++mMa6dRS3OHRxxI5DuzISNDiQX\nGEyCx+xD7oSEUXiPY6k//elP9ZGPfCSHQ1JRT6pFJ5DlCube0dGhQ4cO6fDhw7p582Y2tYmvnZmZ\n0fz8fK6r8ZnPfEbPP/+8zpw5o7W1NY2MjOgnP/mJPvShD+ny5ct6++238xm4HR0deuedd3T48GGd\nPXtWUi1tfHV1VQcOHMgxymNjYzp27Jgef/zxXGufujdu1YAJMzYuXNi4fHGwQBDS3OuLxfjmDub0\nuSTZx51jHg3lEJo7BxGIzA+bJBZFGT0o3mYDYzN1RYTxdD8GfUOYOITi4Z7naQAAIABJREFUC5x5\ncN6U6msBxQCsGcuL9YW/xZ8v1Q6fwYLE4vByHazD3t5edXR05CQtIkYWFhZ06NAh9fX1qa2tTdev\nX8/nHmxs1M6FICqsp6cn18lBmF+9elUTExMNFTPb29v15ptv6urVq9nXQHgyvqbjx4/r9OnT6uvr\nyxvCzMxMg7LiAQI+zow71TIJx+Tejo76Wc9AT26B8dmtYOYrwsIOc8b1wD3wtiMSDge964JeNbzy\nX0j6SUrpR9vX/r2kf55S+rBq5u3bkv71dmNeTyl9XdI51aIafq/YRcQNDXeGpVNMtO+q4JEIJY+u\nceHg1fHQQGI4VbQMeBdOXRf+OEg6Ozv1ve99T88884yefPJJLSwsaGxsLKeeswHgjGJClpaWNDIy\noqmpmiJ4+PDhbL6+/PLLevvtt7W2tqbvf//76u/vzynimGizs7MaGxvLfynAREjllStXsgYDLEMo\n4tGjR3P9IIT77du3dfXq1YZxYzwcHoNhsSSwTDCzWUgwMosKppbqeRBSY/leNlW3rIgK4TrEPKGd\nuSMs+gxck9sr3qYtMdGJvtCPmAkZeTOOA5tbMvyfYnQQPhdMfzReEo/gSxcYCNrXXntNm5ubuVQF\nmwdlATY2NhqehZOX5KehoSEdOnRIhw4dyoeiTE5OanFxURcvXswb8+uvv57zTTjcnBLGU1NTGh4e\n1pUrV7SxsaHJycm8vhYXF3NdpxMnTujgwYM6c+aMenp6skN5aWkpFw1kvNkYXdHzMUUGAMGCuUtq\nOPKzLJeBuXNIOFpSfm+09pwvpEbIkufw/2YHmDSj3UTdfE9Smc3xrR1+80VJX9xtI1j0zuwudB2r\nctOdQS7D9H3D8MGM5FqKtb8BH/V2bW1t5dre58+f1+Liok6fPp2vERNMmFdbW1t2jLFAtra2dPLk\nyRz3jrf/2Wef1RNPPKEXX3wxV+pDy29vb8+Cn/Tx8+fP6+rVq7p9+7beeustFUWho0ePanNzU4cO\nHdLMzExO3z506JAee+yxBgecVItaWVhYyFmVHR0dOQZZqkNkCGyPAIGhXSP3ZBDmJQpqnhu/j/Po\nv3FNJzp9WVDubIsZhmX0IHhbqtfcd0EuKUd8EA3CeBJBZu/MG68LF8YFjN1PjGJzYRNgHaEwsFEw\nnsy9VBvPn/70p1pdXdXRo0d18uTJ/FxS7yk90NPTkzNCsR6OHz+eyyasra3p5MmTGhoa0ptvvqnX\nX389hwZSiZOxqFaruWBaZ2enpqenNTs7q8nJSUk1S3lkZESScvYuG8rRo0dz5A+8ffPmzRwT78qP\n53fgy8BfQv/dMU5GLfzl0Xg+ny7UPaqGOYvwTRTyvhbcOuB5zve7jbaB9kVmLBoHjfcsMo/djoPk\nZi2CJi5utEYfcH9vhGYkNWjyJDY4ZuaF0yYnJ/X9739fv/Irv5K12KIoMg7vjh6OLOM5eNL5f2dn\np1ZWVvTss8/q1q1bmpmZybXqp6enc/o4kEtHR0eu3XHq1Cmtr6/r6NGj+fSdxx9/PC9GyigQL10U\nRS7YBiMTt0xqOu3zmvwklERcnHF2bSTCX1FT9bDUCKdF/oDiput4qvPBvS6E+0VFUc9ARojDzwgK\nL28r1Rc1v6dPDt1Idc3fBbavAXjO8Wj+So2lk8Hsadfa2pqmpqb06quvamJiQsPDw3l+UV7QKgld\nJuwvbfuMeIck9ff36/jx41n4UwQMa5UoG+b0ypUr6unpyYlDKC8TExM5VwBfxtjYmNraagXd4AdK\nIDjcylm4g4OD+ZAU95m0t7c3JC/5CW8Rj2cOnLcZOz/PwuE5t7Yglzv+/GgJuhIUlYDd0L4Q9FJd\nMECO1Ut3HgtHlms0e8oo4nE+UIRexfs9ioOsWRIZCFkrikI9PT361re+pY9+9KMaHx/PCzI6a4aG\nhnTz5k2tr6/r8ccfz7VmgHeYyJGRkRxXf/HiRT3xxBOanJzU+973vgZMc21tLYeajY+Pq729dj5n\npVKLypmZmdGxY8dysTg0MRb/4uKipqen87GEFCBbWFhQtVptiMCJpimRC/zfmR/hDqwTYZOIu/vG\nHPF45w3mOKXU8FwEDc9qBuXsFbHQHRaAD9EawXPdLI9jisbpMCMaPpuJp9q7lcO4eO0mIkLgfcaW\nv5QlOHfunD7wgQ/kLE3fhNi0UCD6+vpy+OX8/HzeANCKR0dHNT4+rq2tLV2/fj2fXIVVsrm5mY8U\nJFzSgxDoX0opJwJizZBDAIR57dq1XBYaaxXh65ubVN9wEerRYpXurJrqvsIIGbo1HBEK7iu7Fp/v\nQp7f3M0R3Iz2jaCHMd1B6g5WdlAGJ+5uznzt7e251gU7NwwZHR3umIrPcmeiDzaLibCpnp4evfrq\nq/rkJz+ZNwCePzAwkOOJh4eHtby8rKtXrzYwGbHP1Jqn0Njx48c1Pz+vI0eOqFqthXCygMbGxlSt\nVhuEfHd3tyYmJtTe3p4PLB8bG2twDlG3n9hkEkcIbYTRmYuomZMd6POAZulz4tEf0RHGcxzSwGHJ\n733M3aRlw4VHeK5v5giO/SDopUboif/D3w6dQL7oPX/E8V/mh2e5soKA9XlyvmdOyhLZHJMmHPfn\nP/+5jh8/rgMHDuR5daglpXrZCcJ0aRdaaU9PTy4FAHTIAStY0I6Jp5Q0PDzcgJmPjIxoaGhIKaVc\nKJD2+xkIrMv19fVsDbDG8IkA3yBQ2Yx8Y/ZYd/oTocrIo24xMZeRyqCeiCr4vWXCvAy92In2jaB3\nwkREQHiCDoMYKxIy4BQE80FgEsqcYL67R1wMk49r6+vrWZv3tiwtLelv/uZv9LGPfSyHm3kYFAu6\nv79fKaXszEW4cSYmNbRHR0czPDI+Pp4dUgi4iYmJXDcE4Xbs2LHsLMKRRDVABCGLC4x/fn4+WwjV\nalU3b95UpVKr9e2mIhDLxsZGdvx6Ig5jdTeB6gvCN1v/nX8uY3K34hBkbn1xj7/vXhbEu03e12hy\ns6m6wiE1JtPQ/gg98tmVE3dAO2bvygSbulQ/HQlByLXNzc2cqDU/P68f/OAHOnbsWE62cn8Nx2ey\n5uBh2jU8PJxjybFUKLhG1A4ltzc3N3MdI+ASrA7+dnR05OQjhLMrIevr6/nMChKecMx6YACfUSBZ\nG6xXh3ZQZCgP7DAx/FymuTNP/hyUmzI+cYXG5RC/9+fcK+0LQe+Nd0HAAHtUQJlTg+tSXfP3KBt2\nyoj3+w7KonHcnufFd3vbKpVKjkT40z/9U33hC1/Imw5WAkWa0P4xM2NIKLjm5ORkxtlZhKOjoxoY\nGMjVM+nD0NBQhrEwY3EGu6lbqVRyhMTCwoLOnTuXk0+6urpyvRFSraPwZFwk5YVH5mFk0mbkgir2\nPQpDtw7iwnBfSpwjJ/et7BWVCYC4yaEIuAIR4RnGHysVXnVlBfjD8wdQDjw6TaqHfBLdBCFAaWN3\nd7euX7+us2fPamRkRKdOncrvrFarOfMYJyeJTWj5zAH3EYAgKW8o/f39Wbv3E8sorYy2DmYOfw4M\nDDRg40SQXbhwIZfT4GyGarWedY314Rq4W1AkTfE9SqLfF52mUt1qirztG0HkU/fB+D0RuYgbgFvQ\nu6F9IeilO0sReAd9UnxgyshNXamuvcfPEJPj2GfUGCHaEXHg7u5u3bp1S/Pz83ruuef067/+6/l7\nYpj7+/vz8Ws4rtCCqfy3tVVL1z58+HCOTKhUKll7J7OW1HM0OBxcMD6HngwMDOTyr5SUvXnzpl5+\n+WVduXJFkjLMhTns1pSPO5ofYXkImah97kSMHX31BLNowjL+/M7hhbL5cz5ynN81/r0iD4X0vjg/\nYXExJg59uPXI87BeWfQOS7I5utBm7GLyWIz/jtm0g4ODuRLrgQMHdPDgQfX39+f5HxwczL+jnSQC\n+rkQQLPEwFOeAZ4HT6dMMRo8fIdfCIvZSylItfU+Nzenc+fOaXJysoGH2Rw8HFdSrkjpwR/O25An\nj/ncOH9KapgnRwj4rfNvhNGirJHKk+P8t81kYBntO0EvNS7wiDNCUWg7gxdF/bQdGBDMjWJAvuuy\nC8ckK5jEyxu72euOLXDNH/7whzp16pSeeuoppZQ0ODio2dnZXH+F/nR3d+vatWvZ9CQKZ2ZmJreJ\nksCEsA0MDGhiYkJXrlzJjEu6ttdfP3jwYHYsFUWhkZGRnP36zW9+M+P0mPTt7e0ZK3VBy2KtVutl\nJpgTL+bGmLg57FAOQoQ2eZJOjFrw+Y+OMM+j4Pcu3HwRuXMzLqC9JBcSCPII3dA3z+dwfvdgACw5\nxtYtTeAh166pceP1hRBs8Xu04N7eXt2+fTsfvPO+971Px48fz21A+3bfCaea9fb25rLIHHZy69at\nBp7Dukgp5bNmNzc386EiwJgoMpQboU5NV1eXLl68qFdeeUUXLlxoqG0DTORjDl/SfmCd4eHhbC04\n5u4WCP0r08wR2hGhYE04GgA5suDz4fwSFZxfRHHZV4Led2cGMw4e16NAlu7cIGCgeJ9Pki88N5X9\nmeB11Wq1wenFbxyOWF1d1Z/8yZ/oE5/4hH7nd35Hc3Nz2QnL/SnVIkfAL1mIUq3W+tbWVj53VlKu\n6McByxzcTWx+V1dX3sDQdKitMTg4mI9d+/M//3PduHEjWxgkTHk8MH1hI2MsPFMQhneBHDWUuBAQ\nQNzv4+tWGxqTM7bDOPwG4eglXp18bvZa0Ds/xXhpqT4ebk15ar5vilhDaL5okX7+abRKPRkOzTq+\np1KpZAEPnOfWZnt7u2ZmZvSd73xH77zzjoaHh3OosFQXmkBHQCQu1Dxc0aOQiqLIz+IaYY7wd1tb\nW94s3AIFsvnud7+rt99+WymlXGpkbm4uWz9siFLd6vPADUk5GIGzlh2ujPMFeR+wrFygowi5nHGY\nxp3gTtzPM2JeiKMfu6F9KeibfS/diXGVXfdF48LBk3kiubCJ19wBXDYh0Tvf09Ojc+fOaXp6WqOj\now1aLAwR37m2ttZgElPBkgXHRrGxsdEQRue4ORX73AnX1dWVk1MmJyfV39+fMyh944ljGhM0fJP1\nDdPnzaMQ/DeuHUmNYWeutfszfXybUdk87uZ3D5pcSfHxcmEQ8WCp+Zi4RuphlF5fPR4gQ94Fmzft\ncUHvFhvtBELkdwsLC7p06ZImJyezYx6h7YelYHWU9RWHJhsNfQJuIvrFoRZ4GZiS5K1qtRZEMDs7\nq6IosoW7vLyco31cm/ax9Ph5lyNu2XoeiStCZcqMz5fLHsfgy+Scj3dUnnZ6x078H2nvzlgL5IwG\nMWDRuSHduTFEAcRvYBrHhl1gueYU/QKQDz6hWD4JnixSrdaSNdbW1vTHf/zHuXSq43h+L0J7a2sr\naxaeOk20ggvmvr6+nEzCAQ6U54XRKWPKCTc/+tGPspNWUs7cxZJg/KOm4Q5e4pnR1Hzx+kbnvhTf\nKKJlxmJAA3Sh71pp3EzKnObN+Cni23tBCBQojoFr+2UQDvf7+MC7joEzFg79ML+U5HWFAw2Xdnh2\nrltfRJERunjx4kX99V//tc6dO5fv55k9PT1ZW2ZjYRNwqw7+o52sK6DKkZGRHB+PYoA1C+/Tnp/9\n7GcNdXtYf6xtD79lA/FD1+E/P86R8WSz8Sqjrp2XyYyovfP8OL/MFZuLjzkOd57N9zE4ZLe0rwQ9\ng+YF/xko1xKd8TFrdtLoXauIQtwFQtyli6LITA+W6nHmtGFxcTFXjCQBqihqOOULL7yg4eHhPNHe\n9uHh4Yw5joyM5IXiccwIf3B9FgKE3wEHFRFAbCjg+2fPns1jmVLKGYmuXUEIcdfSEPRLS0v5/Yyv\nJz/F8fVn+xgwvi7odtJg4uKoVOrlGHbiqTKz+EFS3Oh8oce2Oc83e45Dmg4DwacuqF2IRSgLSAhh\nxlz7piMphyuSvYr2funSJZ07dy4XM/ONF97u7OxsOCYQvmG9EgUm1XiDSLPY3v7+/pw4hcUzODio\n1dVVzczM6K233srjtLq6msuEeHSSb6woj7EWEpsF90HOR55EWKZk8F1ZCKXUaNk4X5QpA/6Xdse2\n7Zb2BXSDqQchpF2j4280c13TcwGFI5Fj9RYWFnIJX+AQdmfMXn7neJtrquzIzvC0G+3YMwg3Njb0\n0ksv6cCBA/r0pz+dNZChoaHMsG4uEyqJ9tDT05MZZ3l5ucGZLEkHDhxosBZSSrlGDkfIfe1rX9O1\na9e0trbWcFg0At/hGxZ/URTZEqLODhrY4OCgpHpoHBsgcwB8gBUSow/4bRQ0vrjjpg504Bu6Y6Mu\n6PjsoYt7TbGtjrW70Odeh2+itcT3OE07Ojqy0xMe9zWysrKS8XzGhs3aFRi0YXeku/VLTHp3d7fW\n1tZ0+/Ztvfjii+rt7dWzzz6r0dHRhpOt+vr6dOPGjZw7wvxiZbAG0fQdHnIlBd4kKKIoinze7Xe+\n8x1NT09rcnJSIyMj+R6CI1irUr3+j1SHJj3Jisgy2umngMU55DO8HQMKkEUuzKV64EHkDda7P9s3\nTo/04b1RSbob7QtB7+Twy71QGSzgQt8nwYW4C7wyTQqm9123KIp8Wg/CG8Yi8kBSXhTPPfec1tbW\n9Fu/9VsNad4UHKPdOL6IxPFjDnk2Dti2trZsikt1AYEzltLFFy9eVLVacygvLCzkeGaYFAdd1CYc\nq2QzJFLCmT5CKm7uRqyyjHx8wUMjsRE4HOQYps93mUa113h9tCRdYfHN1aGYqFFCsX/8Br5xAQBv\nkegDrOFWA22CvzgeEsgHjRvHJxtnf3+/bt26peeff16VSkWf+tSnGjKfwcddcVpZWWkoLcxc4ovy\nEM2VlZWGI/PgUX536dIlvfHGG9rY2NDAwEA+e4GjPJ33PLTVE69Q9FDW+J3zryuZfOfPdtniSodD\nO8y3b5zutPVaR24hs+k6b/tGcS98vW8EvZv9vjAYqLt1KmLF/iw3kYFfPH67THvy58Jg/Ka9vT1n\n6CFci6IWprW8vJwdpWi2HR0deuGFFzQ/P69PfOIT+qVf+iUtLS01WAySciIVDOmbBosF3JKNgMWF\ndgZVq1U999xzDScJDQ4OlpqUPtZRC/ENMW6KMCXf+TNce9rtpt1sQ8BSIMzVcXcWikeU+Bjcq8Lw\nbpMLdcdYEQhRkJR9F58FefQTY7S6utpwJCTJeh5ZhebLd2iywI5ra2v5nF0K23ECVLQK19bW9O1v\nf1vz8/N66qmn9PGPf1xLS0va3NzMmjeKBps4QQ3AOZVKJZ/fQHXVoaEhtbe3Z2UnpZSzvWdmZvR3\nf/d3mpmZyWc6oP1TDz+llKFGomi2tuqVKN234Fg9zmc2jEqlkk+Mq1QqOf7fBXYZlBOVKcYecrQC\n3vXfRDTDN45fBL7ZN4L+flDZInfBUzY5cQBdC2PxeFiW+xXcUQuBT1YqFZ0/f16SdPr06azJIRAx\nN12zdqELU6KNuPXiWgObwQ9/+ENdv349ayf8ixpzHKNoEfHZD672zbTZOO1WwPrGU4Z5+rMd6mhG\njIe3YS+FfYShdvo+KjcoFu7087++4fLZ4Rd/b8yR8N/zHg8pdG0U7beMtwnzvXDhgiTp/e9/fw7d\njZnoWBjReoRHgZAk5XMPvG/kAvzsZz/Lh4ADMXouiVvxPvf0nXwBt4qkumIQedzXl8+hW2k+l86v\nDhn58+J9ruCiXEWe2a3SW0b7QtDTGR9oOuvJSL6T+cKQ6vVc+J7JWl9fz1oJBZjABJ2ZXHOIi46/\nHqUyNzenwcHBbPJiEre3106dX1lZyaV+K5VKNolffPFFdXd361Of+lRD7Q7HkumLJyBxva2tLTM3\n2oX3Y21tTfPz8/rqV7/aoOWCr6LFcT3ihj7GDsUwpow3C2pzczOb1ZjAruX4OKIBsjDLrCfgG198\nbFDeLhJvyuKW/XlxMT5oisLdhUEUBJH/cPw7Tux8wabuCkpbW1vmPfD43t5eLS8vN0BFwIAIT0kZ\nlmNtsLlz6heavYdBEr0yPT2di/f92q/9WvYBwHuceeowKHAl7aH9YOtLS0u5Ng/O2tdff13f/OY3\n84HgUj1xyqtpMmZo6bTD54Sx8PBpfHGsL/c7OZ9FwX83BQcrNJYu4HfuS2Bu3XKFZ35RXt4Xgl66\nM2Y4Clq/R7pzAcVBZjIQRH4tvtMFjmP7UmM9EqnOODhyIN7D74iogXnI0Ovs7NSLL76ovr4+9ff3\n6+TJk+ro6NBjjz2Wf7u0tCSpfqINzAFjxgO0PTqpv79fzz//vJaXl/ORaETM8LxocsKwjDXaFQIE\nS4Kx883HrYXIwGVMGRN6fNwjjOELyp1U0TnlcxkhkP1CkQ/pL+PqGjff01cEVOwzApAN3Z+J8ASm\nYVzc6oyhjyRMAQmC1ePgLIpaUEBfX58GBga0tLSUNwtw9Zdeeknt7e06ePCgjhw5op6ennyerFQv\n5oalS3vgN/xOMWNbkubn53X+/PkMN9FuNgO0esaUEEvGCQhNqkMrLgN8HTi029XVlQsIllnSUJlM\nghw64/280+9zpYq/kZ+d13dL+0LQx0Xpu6M73XyAd3qGa0YssGhGRpwrCgVnABaSa9q0ietoRltb\ntdoZhw8f1ubmpt544w21t7draGgoC9rOzk699dZbeuaZZ/TGG2+ot7dXb775pnp7ezU8PJwPCoEx\n+R3ak5t49ItFPTk5qe9973v5rFjikMnaZTHTRzQaZ0D6XalUGuAkNx3jeEWooAwG4z6ewUJzq8Kj\nPnietwdh5nh8M/jJtce9IvjMN08vo+Fj6b4pNm7Gx687XOPrwTVZrE93RvpvcIB61BSQxvr6es7P\nIBoFTXloaEijo6P5tDNwcTTe9fV1TU1N6eDBgzlTlSicwcHBXNSPKBtf55TVcH7gjNm1tTW98sor\neu212vG9bDRu/VHKAIraN74mh6Y8Wxa+cquGcXHFJ/rDPGzaN2innWSPQ1TO7/CPt8/56l4UmX0h\n6KXGDEkEE9d9MTQT9mWbhQsv4I14P4swDqiHBfomQWo2E0+5ARZVW1ubZmdncwkDNAJ+w2K6cOGC\nPvzhD6urqytHImBiLy4u6vLly1kTd3iIqBlJWeOB5ubm9OUvfzlr/UNDQ7p9+3a2PtD0WJhuppbh\nfy44fMzKog18UTXTNHzj9kifCPO4E85xVaITPBLBtTJ/N31hs9pL8oSdKKTZxD25CAHL3Hjstmuk\nOME5DId5xkHt8yvVcy6AUrxKqdRYjprNBSEkKbd3dnZW169fz6GbbkWAoX/wgx/MChBtvX37dj4c\nh/eT5Le5WTtjAZhudHQ0h45ubGxodnZWP/jBD3T16tVc1ZWNELyd5yGosYZQbhg/eC9Cws7DMSfB\nNXKH0+K6gbejL8kVH1dAmC9kkCsp0QKJ62GntXYHD97thpRSt6TvSuravv9/FkXxH1JKo5K+Jumk\nagco/2ZRFDe3f/MFSb8taUvSvy2K4v/u9A46hebhDsMYWeC/cTPKBXfU9OIO684lNhYmOgowx8c9\nc9CjUdCQeMfhw4clKce4e8IXDNPe3p4PGMH0BBf16BIYk0iGlZUVrays5P739/drdnZWfX19unDh\ngq5fv55zB1ZXVxsYCdOWmh60LQr8oihyXsHGxkZDUTSYOoaEMa4IE+7xeHofXw8LjDDUNg9l8z7y\nAP+aafQQ9zSrh/OgeFtqzIBkDLgGhEH/4Jfoj4qWLaG9bW1tOS7dhYHXWCevwhOC4H1JDbWMiFKh\n/S7UOOjGE50QnB56eOPGDR06dChj575ONzc3M4aP8F9bW9Pk5GRel/D2/Py8FhcXNT8/r0uXLmXl\nhxwBlBE2GtYJ4+gbv/MubUUW+FrzwIgItTC+zJFbjn4vz+M3DgVzj/Mpgt83HH+28xHz0gweLaPd\npAyuSfrHRVF8SNKHJf1qSunjkj4v6YWiKM5IemH7/0opPS3ps5I+IOlXJf2XlNI92c6uGd4LDlX2\njJ2+9/uYnN1QnAipcVOg8BKhX7zHNdbl5eUGZ5NvbmhCaGloIzCYH58Gg3AuqWvJUaPjejNyzZgQ\nOAS6RwZEBovPLINs3i26l2dH+KeEHghvN8Nx4TvnVR9rVzju9kwXJHHtwCO+ocT1EQWLb/o826Gd\nlFK2Nr2NbuXG9sd+stnAp/C2hzNj3ccSD0CO7qNgE3ULxN8Vr0UL1vvv93rf4vjv9LeM7/z9O83p\nbr67F+jmrpKtqNHt7f92bP8rJH1G0le2r39F0m9sf/6MpL8oimKtKIqLkt6U9LFdt0iNC6CZAPZJ\niBo9g+KhhUyq78puTpU5Fd3SYNdPKTXUZHenCcxGdiJHnXkEEff39vbqwoUL+RqHjsD01AxhA3HN\nlMxCIi66u7s1PT2dQ86q1WpOL49aoTtVfbx90+Ia7bl69WrW+KKAd8Z1TaaMMZ3547Mgb6/DHXzn\n4ah3I3c6ltGD4m23zvzaTuMRr7uwdD6lb2DLwDGOR0tq8LVIdWsH/nKh7t/RDg80QDFxaGlraytH\nXXV0dGhycjIfauKbD8qDr0dXHogOI969u7tbN27c0DvvvJP75BYpY4JVY3ObP3s0jTthV1ZWtLi4\n2FDrnrHxPrs1EDfJZsK2zI/lFGVaVEriO3xT9H+7pV2psCmltpTSjyRdl/TtoihekjRRFMW17Vum\nJU1sfz4iadJ+fmX7Wnzm76aUXkkpvdIsiYe/zQYsCvncqUqlgal9kOKCQRj4oEXM3s1qBt8z+xBG\nbBxo59TtQNPwYmbAMGgjnkQC0/EOFlFXV5d6enpyTRue3dbWpqmpKc3Ozjb4E1wbgzwJi7Hhr98L\n7okVgTBwvDnOgY/B3QS9z3GcU0l3WCY+xy50mpE/u4y/rE0PhLfLNFm/DrGZeZ/jBhCVEVdyXDEC\n2pEao0zc2elj6dBD1L65TluoYSMpa+JAbUVR3BEy7MLe+0G74W1CNoGYNjY28lGALuBc6MEr0adE\n2xH0jBfX3TL1trlz2udhJ7gwohBlGn3ZevR2ulIXN/dmz9wt7cpqGD5OAAASCklEQVQZWxTFlqQP\np5SGJf2vlNIHw/dFSumeYtmKoviSpC9JUldXV8Nvy3D2kt9LatR8ysjNzmgSw3y+OKKZFx0iaE3O\nsDiCcCThSCReHZz09u2a8uihXjdv3tSJEydyXRs0GcLjKpVK/s61rY2NjYaQzsXFxRwG59qcRw6g\nuURhGzX6lFKGnCRpcHCwAV4q0/4YHyygMivsbkK+7LpDGXGefKGWPYe27STo7zdvd3Z2FrGNPtZu\ndUQBG+91xYJ5g1/deer3Mv/wqZeZQHnge9dY/ZqHgPrG4PVkcO4D5dy+fbshdj+llAMH/CQtNoue\nnp6sqUPUV8I57HH5OOw9cMPHymUIygmaP210a4Mx9PyNZptSnIM4V/5d2ebmvq04l1HJ9O+jzNst\n1CzdY9RNURTzKaW/VQ2ffCeldKgoimsppUOqaUSSNCXpmP3s6Pa1nZ6bd1GcRlyX6nAGXmoWMd9J\n9UFxyIeBc/yScKwYA4+DB6aQagNJHDr/5yxW3s07ndloq18nWoe2wWBeMkFSXoTg7/Szp6cnFzbj\n3cQbr66u6tatW9mJxm88GQfN3NsYtZw45kToYG24UzmG58GoPp4waJk14BAP80Q7I6WUsmM3Qmm0\nOWq59MHHcCe6X7xN+yME6ZaKa+llCk6ZOR/nzkMxfUMA23ZIB2GH05+58WAD3sczEDixsiywjc+x\npAalyvmD/0PxEO44XviyfANjTXv/Yrlt7vVcAxek0anpYyipYQPhPk8YdO28TIHxzSFS5EfG2RWo\nOOdlm/y90F1XQErpwLa2o5RSj6R/Kumnkr4h6XPbt31O0v/e/vwNSZ9NKXWllE5JOiPp5V28J3+O\ngwPE4jg4Gm1cGNHMd1OY0DKYAVMWTRyNGqHP4iOWGGy+DMv3d/JeBBLOK+7d2NjQ8vJyTvJYWFjQ\n7du3c8U+Npauri4NDg6qr68vY5COTZIQsrS0lKNbfIycUaMjif7vFGPuCzRaWd5/f4fXBPJ37CRs\n3TQuu8/hII+9jmPejJotigfB2y7YyqxPV1g8PDJqh7G/vlFI9axpj0JBsHnRLldafO49tt8jSry9\nzgu0N/LYxsZGrgHV1tbWUHUV521bW1uGaKhT41YuUCZWcYReGCf3U8SgAwRj1MRdqPLO6MtBeaGt\nEPfHd/hG7eRzVgYplUGcHp3VzBKMc78b2o1Gf0jSV1ItuqAi6etFUfyflNKLkr6eUvptSZck/eZ2\nY15PKX1d0jlJm5J+b9s8bkq+g8fFELWcnXazZvgXv4+TEU1/IlmIM4/px2WOPbck/N6yRR3NsEql\nVmubg0vQimACMHoWp0MnvlBdqEaYwh1LMKprwrGNZVSmacaxZHy43gynL3u2My1jEGEa77f/3y0J\np10ugvvO295O/3/ZIvbvy/pQdk/Zu6KpXxRFLiEg1QUZm2a0elwoIgjLFBtvl883kCEx8ihUbnFI\ndcUgOjmjVV5mlfkaQ1BL9UNM4hiUadGRmt3L/dFy3Q2VySvvT5lVEP/fjHfeVUFfFMXfS/pIyfVZ\nSf+kyW++KOmLu26FVCrkIR8YBjwKK9/xnenQEHiHtVFS3SNfqVQ0NjamlZUVLSwsZG0cGII6Ofwm\nmrfeVu9TZI7Yl8HBQQ0MDGh4eDiXGJ6dnc0av6d2kxkLdslzORrQmdEFPG1xTXEnhyD3u5YXnUSu\nzUA41YABsKZivyO54IjPi/Pl/WjWdu4va2O454HwtnRnKnu0ivz/zUz+qGU7XzG2nlmMVceJTNVq\nNTtJ8R95mWuPh4/j7GvKlYoyxQdNeGBgQENDQxocHFR/f782Nja0uLiY+ReoFO2f97ll4xi9wzye\n3Z0MonGeiXIgKkIOJboF7AqEW2Q+T2XzU8Zrvt5ok8+7Ky5xjfJM/pZZdrulfZEZS6Opb+GLwgcv\nZus5rumC3oWvayU4Nz3lGBxaqjuEKM7kMI7UKPBc2+A9Pnm0k+toNdzb2dmpxx57TO3t7Q014oui\nyCf2FEX9DMyenp5co5v09sXFRbW3t+fDwx1igYnZlOirZ4nSTk9qYiwdNyeSJ46ZF4yCfIH4onLh\n5s+PTnIfx2iesqCjxVQmbHj2bqyKB0Fx0yrTHrnmcIjzctl48CyP0PLNAgsVv9L8/LyKomgoOuaC\ny/1afHaB6HPk/hmHQTo6OnTw4EGNjIxkR65XpXShR6CCY/3wTXd3t1ZWVhqE4+bmZs498THjGd4f\n2uw+P5cVjCHz4NaLK0wReuO50THLO/y6j5s/w8c7wqLcT5+j5RzftxvaF4Jeqg90Gfzg1GzhkhkY\nhRQDBSOUaf5oOmfPntX4+Hj+3W5NtLixRLPW2wFtbm7qzJkzGhgY0OLiotra2vLRfiRaIXhTSjnC\nwLM80Z4XFhbuEBwunMEbm/WnDFqIwth/C+PH50WmbvZ8p7KFVNa+nRjaBVAz62AvCQ0ZzVFqrhjw\nnWv3Zea6CwHP5UCQoqFL0uzsrG7cuNEQvcXmEDdOfx9/EegIUd5Fe+AXd/aePHkyx7y7VVmpVDI2\nD5GE5VmxjMOtW7eyJs87pHqwQlE0Zj67oGxra8uKCJmz3mZ8AfgDUOp8TOk/yVlYq2Xrnflw2LHM\n6RvXzU6CPN5X9m83tK8E/U6Owd0uYDfF0ODLEkX8mYRASspRNRFD24lcwPiO7e31zadarRWCevLJ\nJ3ORp87Ozpw0hXOVEgowc0opazgsVEm6fv16drSRkeghZXfrS5nm4PH4/NbviZqla+fujPV+Nxu7\nuzErz24m7BFAronGudhL8o2smUbugrWMh1wTLRMokeC5ra0t9ff3ZyjQNf+oVJW1zS1g7vFn+/sJ\nPDh8+LBOnz6tgYEBpVQLq+SYzOXl5Ybqq1tbtbpMnEnLc4mQm52dzXASv0PTj5sQ7fb+u7XBNfoF\nj7vCx3N4P98Bo/KbsjXv49ZMg/f7pDtLK5RZCXEjKPt8N9o3gh5Gbsa4zZwWEJEFcXd17ROh7xBE\nSqnhKEB2fzDw3eyYcdLLFm+cIHD5lZUVjYyM5IOTU0oaGBhoOLKPxXbjxo0GDR/mXVlZUWdnZ0MG\nIAQsxYKmDnmzftC+iB/7Zy9I5r9zhxjj55ZVMyrzX9ztXqfI8JEH9lrQS42wXxTkZZsm30dhCsU+\neXy4F4SLdYIoFOYOUteUHfpx4edWkysasQ/ValXj4+Pq6+uTpBxpAxSKU5i8k2q1qpWVFc3NzeW4\newhfGePi/fJwSQ+c8Dn39cNYuJWMUgBFyIfn+ZwB6Xi/I1wW4ZeoJDWbyzJIyS04h4rvlXYfcX+f\nqZm5UkZ3EwZRYPDZNVf/nv97HG3EQ3fT/nuhgYGBhjM1XTNxrRScfXV1NVfyY5Pyw43JTnRiAXv/\nd9IAd+pbGTTiFJ+7W4a81/G+l3HeLxp97FvZxrSTtera4U6me7NN1Tdt3hcVp7IxihZFszbGDbWn\np0e9vb13wEE+Hjg/qeVEsp8nZXnyH5ZImWbsCVCx/XHs4qZUpi3fTZPejdC+V7oXAX4vkA20LzT6\noqifMg+5VuN1ZqQ7tZ6y58EoCHCpLviWl5cbMNC1tbUcWYNmDFN4DDzv9t2d57o24KYkhMlHItEv\n//IvS6plnXZ0dOQTl3ivRzSAX9IXEls6Ojp07dq17BT10sNS42EoDqWUefbRcPg/2g/mdByD6Fzk\n+bSTqoCe3ETffd7c2edzHAXRTpp5M8FDO++mGNxP8n5626TGPkbBvZPgpV/Of1iq8AYWn9ekYU0w\nlmDb/L5ZmYKyTbxMmSqKmvP3/e9/fy7/ASxZ1lfP+eA7qa41Ly4uNhQz4z1ARG6tYL3HyBlfT/4M\nqX7Osjt6sWaj85m1Hfsd/Yl+bxxP72P8jc9vs/vK3rNb2heCXqrHeXvYFH8d642mFBRjyssWlFSe\nOATTl8E/vqE4NBF3eJ7tm5ULVUxVqZY6fuDAgXzqFO8l2gYG9IOMEdaYiSSdcIhzSvXIhmjGl/WX\nPjVjKMe845hEYVCmLcaFwnj4+HvfdqIYlfAoUJllFMcYimMdlR4XQA67oVxQ3K4oGs8j9fujIPZN\nxWGRWEIZcqtxdHRUUl2Qlq0VeDiGnXrwAMIcnxnwqq8Hb7Nv7lHYRnL/ROTnsnnw5+12fuM8l7XD\n19duBP1Oa3Yn2teCnsF1Z2Iz89R30ihYI/blwgbPvHv7/b0IW3+2M+VOjs64ScCgRNWgAXGvRw84\nI1ar9XhiMmTRwBYWFnK4WXd3t27dupU1aMd36TfvJxphN7hf1Pabjb8Ld2datwx87FmsjpXuBAvd\nC7y3n8jnPo5NpDKh6DwXN1qp8Vg690Gh4bK2pDoG71q8+6u8vZG3PUzR+cl/Awbvgr8oioYzmbkf\nWNItUcJ8Ke/hY+Ghl27lw18oOzwv+pl8vPx6VAgZwzIlxqNoojB3OeHroWxjjHN8t++dHHra7XrY\nF4IeswnmYpBcuNxtJ2MSHEbh/hgeKDVONn99c5DurHrpHnqe4REmrnE7o0uNJ80Tn094JCWAcarC\n7FH7BQ6pVmt1bvr6+jQzM9MAmWAhoA05VgrTra6u3iG4m82Lz0fsU/R5xDGOTFiGCzvMtduoq4eN\n7uaM454yiMk3wDLowC2osjIA/GVtRQHlvO1hoNwPb8XEO57r9ZNSqoUo9vf353BG1iV+JObb+Zu2\n+9qpVmshzw6NcEg3G0BcJ7wLCMaLD97NWvI5cJ6mz1ERdCqzcsvmoJmSxLUyYb8Tz9+LZr8vBL2k\nBq0DLzpmIjidC4Vm0EnEeRHGLAa+c089hxXTDp/ktbW1fNQZ92NOgod6/DDvjUlArg2QGAa2TklW\nsFX659qD15anzbOzs7lfnZ2dWlxcbIBcqI3D2EBlUTFuRvvYReEO0VbXVvmda0YONTls5OY341CW\naelz7JpRUdwZ9eEa1C9i3t5Pcm00Wo7SnQ5Lvm8mHMpgnzJtV6oJSNcwmcuNjY2cSOW1Ztyng4CH\nR3mXr0kXYrwX4ehRKs4rKF+cgubPjRapK3FSXSFwnvF+xb/NhCjfRY08zlfZ+Jddj7CLj0mzuYub\nh1vEfn9EJcosu50o7QctKaU0I2lJ0o29bst9oHG1+rUf6ERRFAce9EtTSrckvfGg3/uA6GHjgd3S\nw9SvXfH1vhD0kpRSeqUoio/udTvebWr1671Nj/I4Pap9exT7tW/i6FvUoha1qEX3h1qCvkUtalGL\nHnHaT4L+S3vdgPtErX69t+lRHqdHtW+PXL/2DUbfoha1qEUtuj+0nzT6FrWoRS1q0X2glqBvUYta\n1KJHnPZc0KeUfjWl9EZK6c2U0uf3uj33Siml/5ZSup5Ses2ujaaUvp1SurD9d8S++8J2X99IKX1y\nb1q9M6WUjqWU/jaldC6l9HpK6d9tX3+o+/Wg6WHm7UeRr6X3MG/HrLAH+U9Sm6S3JJ2W1Cnpx5Ke\n3ss2/QJ9+EeSnpH0ml37T5I+v/3585L+4/bnp7f72CXp1Hbf2/a6DyV9OiTpme3PA5J+tt32h7pf\nD3gMH2refhT5erut70ne3muN/mOS3iyK4udFUaxL+gtJn9njNt0TFUXxXUlz4fJnJH1l+/NXJP2G\nXf+LoijWiqK4KOlN1cZgX1FRFNeKoji7/fmWpPOSjugh79cDpoeatx9Fvpbeu7y914L+iKRJ+/+V\n7WsPO00URXFt+/O0pIntzw9df1NKJyV9RNJLeoT69QDoURyTR2r+30u8vdeC/pGnomb/PZQxrCml\nfkl/Ken3i6JY9O8e5n616P+fHvb5f6/x9l4L+ilJx+z/R7evPez0TkrpkCRt/72+ff2h6W9KqUO1\nhfDVoij+avvyQ9+vB0iP4pg8EvP/XuTtvRb0P5B0JqV0KqXUKemzkr6xx216N+gbkj63/flzkv63\nXf9sSqkrpXRK0hlJL+9B+3akVKt9+meSzhdF8Uf21UPdrwdMjyJvP/Tz/57l7b32Bkv6tGqe77ck\n/cFet+cXaP//kHRN0oZq+N1vSxqT9IKkC5K+I2nU7v+D7b6+IelTe93+Jn36h6qZrn8v6Ufb/z79\nsPdrD8bxoeXtR5Gvt9v5nuTtVgmEFrWoRS16xGmvoZsWtahFLWrRfaaWoG9Ri1rUokecWoK+RS1q\nUYsecWoJ+ha1qEUtesSpJehb1KIWtegRp5agb1GLWtSiR5xagr5FLWpRix5x+n8JzApfnnoMMAAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x261d4630d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# face\n",
    "lr = 50\n",
    "face_lr = low_rank_approx(face, lr)\n",
    "plt.subplot(121)\n",
    "plt.imshow(face)\n",
    "plt.set_cmap('gray')\n",
    "plt.title('Original image')\n",
    "plt.subplot(122)\n",
    "plt.imshow(face_lr)\n",
    "plt.set_cmap('gray')\n",
    "plt.title('low rank=%d' % lr)\n",
    "plt.show()\n",
    "# about 50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IPASj/yNSQkKiCwR81Qzvgx7XT8Ta3WBE4N6KAvR5Ok7yFOi9T/u8tZasDdDv7u4uYtdc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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x261d45380b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# sky\n",
    "lr = 15\n",
    "sky_lr = low_rank_approx(sky, lr)\n",
    "plt.subplot(121)\n",
    "plt.imshow(sky)\n",
    "plt.set_cmap('gray')\n",
    "plt.title('Original image')\n",
    "plt.subplot(122)\n",
    "plt.imshow(sky_lr)\n",
    "plt.set_cmap('gray')\n",
    "plt.title('low rank=%d' % lr)\n",
    "plt.show()\n",
    "# about 15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
